Projectile Playground

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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">
<title>Projectile Playground — sloprun.dev</title>
<style>
/* ── sloprun design tokens (verbatim from demos/tokens.css) ───────────────── */
:root {
  --bg: #F6F6F3;          /* neutral paper, not cream */
  --surface: #FFFFFF;
  --ink: #1A1D21;
  --muted: #5A6068;
  --line: #E3E2DC;
  --accent: #C05600;      /* phosphor amber, darkened for light bg */
  --accent-soft: #FFF3E6;
  --run: #1A7F37;         /* earned green */
  --run-soft: #E7F4EA;
  --danger: #C93C37;
  --radius: 10px;
  --font-sans: system-ui, -apple-system, "Segoe UI", sans-serif;
  --font-mono: ui-monospace, "SF Mono", "Cascadia Code", Menlo, Consolas, monospace;
}
@media (prefers-color-scheme: dark) {
  :root:not([data-theme="light"]) {
    --bg: #14161A; --surface: #1C1F26; --ink: #E8E6E1; --muted: #9AA0A8;
    --line: #2A2E36; --accent: #FFB454; --accent-soft: #2A2118;
    --run: #3FB950; --run-soft: #16281B; --danger: #F47067;
  }
}
:root[data-theme="dark"] {
  --bg: #14161A; --surface: #1C1F26; --ink: #E8E6E1; --muted: #9AA0A8;
  --line: #2A2E36; --accent: #FFB454; --accent-soft: #2A2118;
  --run: #3FB950; --run-soft: #16281B; --danger: #F47067;
}
body { background: var(--bg); color: var(--ink); font-family: var(--font-sans); }
/* ── end tokens ───────────────────────────────────────────────────────────── */

/* demo-local additions (scrims need alpha; tokens are opaque hex) */
:root { --scrim: rgba(246,246,243,.93); --shadow: 0 1px 2px rgba(26,29,33,.05); }
@media (prefers-color-scheme: dark) {
  :root:not([data-theme="light"]) { --scrim: rgba(20,22,26,.93); --shadow: 0 1px 2px rgba(0,0,0,.35); }
}
:root[data-theme="dark"] { --scrim: rgba(20,22,26,.93); --shadow: 0 1px 2px rgba(0,0,0,.35); }

* { box-sizing: border-box; }
html, body { margin: 0; padding: 0; }
html { -webkit-text-size-adjust: 100%; }
body { min-height: 100%; overflow-x: hidden; }

.wrap { max-width: 1160px; margin: 0 auto; padding: 22px 16px 26px; display: flex; flex-direction: column; gap: 16px; }

h1 { margin: 0 0 6px; font-size: clamp(21px, 3.6vw, 29px); letter-spacing: -.021em; line-height: 1.15; }
.lede { margin: 0; max-width: 70ch; color: var(--muted); font-size: 14.5px; line-height: 1.55; }
.lede b { color: var(--ink); font-weight: 600; }

.stage { display: grid; grid-template-columns: minmax(0,1fr) 312px; gap: 16px; align-items: start; }
.left { display: flex; flex-direction: column; gap: 12px; min-width: 0; }
.subgrid { display: grid; grid-template-columns: repeat(auto-fit, minmax(258px, 1fr)); gap: 12px; align-items: start; }
.field {
  position: relative; overflow: hidden;
  border: 1px solid var(--line); border-radius: var(--radius);
  background: var(--surface); box-shadow: var(--shadow);
  height: clamp(300px, calc(100vh - 330px), 500px);
  transition: height .22s ease;
}
@media (max-width: 940px) { .field { height: clamp(240px, 46vh, 400px); } }
canvas { display: block; position: absolute; inset: 0; width: 100%; height: 100%; touch-action: manipulation; outline: none; }
#sky { cursor: crosshair; }
#sky:focus-visible { outline: 2px solid var(--accent); outline-offset: -3px; }

/* the drag-to-aim grab zone: owns touch so the rest of the page still scrolls */
.grab {
  position: absolute; width: 92px; height: 92px; margin: -46px 0 0 -46px;
  border-radius: 50%; touch-action: none; z-index: 3; cursor: grab;
  background: transparent;
}
.grab:active { cursor: grabbing; }

.hint {
  position: absolute; left: 10px; top: 10px; pointer-events: none; z-index: 4;
  font-family: var(--font-mono); font-size: 11px; letter-spacing: .01em;
  color: var(--muted); background: var(--scrim);
  border: 1px solid var(--line); border-radius: 999px; padding: 5px 10px;
  transition: opacity .5s ease; max-width: calc(100% - 20px);
}
.hint.gone { opacity: 0; }

.legend {
  position: absolute; right: 10px; top: 10px; z-index: 4; pointer-events: none;
  display: flex; flex-direction: column; gap: 5px; align-items: flex-end;
  background: var(--scrim); border: 1px solid var(--line); border-radius: 8px; padding: 6px 9px;
}
.lg { display: inline-flex; align-items: center; gap: 7px; font-family: var(--font-mono); font-size: 10.5px; color: var(--muted); }
.lg .sw { width: 16px; height: 0; border-top-width: 2px; border-top-style: solid; flex: none; }
.lg.off { display: none; }
@media (max-width: 460px) { .legend { display: none; } }

.toolbar { display: flex; flex-wrap: wrap; align-items: center; gap: 8px; padding: 9px 11px; }
.tbnote { font-size: 12px; color: var(--muted); margin-left: auto; }
.tbnote b { color: var(--ink); font-weight: 600; font-family: var(--font-mono); font-size: 11.5px; }
@media (max-width: 820px) { .tbnote { display: none; } }

.panel { display: flex; flex-direction: column; gap: 12px; min-width: 0; }
.card { background: var(--surface); border: 1px solid var(--line); border-radius: var(--radius); padding: 12px 13px; box-shadow: var(--shadow); }
.card h2 {
  margin: 0 0 10px; font-family: var(--font-mono); font-size: 10.5px;
  letter-spacing: .1em; text-transform: uppercase; color: var(--muted); font-weight: 600;
  display: flex; align-items: center; justify-content: space-between; gap: 8px;
}
.card h2 .aux { font-size: 10px; letter-spacing: .06em; text-transform: none; }

/* readout table */
.tbl { display: grid; grid-template-columns: auto minmax(0,1fr) minmax(0,1fr); gap: 6px 10px; align-items: baseline; }
.tbl.solo { grid-template-columns: auto minmax(0,1fr); }
.tbl.solo .air { display: none; }
.tbl .th { font-family: var(--font-mono); font-size: 9.5px; letter-spacing: .085em; text-transform: uppercase; color: var(--muted); text-align: right; padding-bottom: 2px; }
.tbl .th.hi { color: var(--accent); }
.tbl .rk { font-family: var(--font-mono); font-size: 9.5px; letter-spacing: .085em; text-transform: uppercase; color: var(--muted); }
.tbl .rv { font-family: var(--font-mono); font-size: 14px; font-variant-numeric: tabular-nums; text-align: right; color: var(--muted); white-space: nowrap; }
.tbl .rv.hi { color: var(--accent); font-size: 15px; }
.tbl .rv .u { font-size: 10px; margin-left: 2px; opacity: .8; }

.pill {
  display: inline-flex; align-items: center; gap: 6px; margin-top: 12px;
  font-family: var(--font-mono); font-size: 11px; letter-spacing: .04em;
  padding: 4px 10px 4px 8px; border-radius: 999px;
  border: 1px solid var(--line); color: var(--muted); background: var(--bg); max-width: 100%;
}
.pill .dot { width: 7px; height: 7px; border-radius: 50%; background: var(--muted); flex: none; }
.pill.busy { color: var(--accent); background: var(--accent-soft); border-color: transparent; }
.pill.busy .dot { background: var(--accent); animation: blip 1s steps(2, end) infinite; }
.pill.ok { color: var(--run); background: var(--run-soft); border-color: transparent; font-weight: 600; }
.pill.ok .dot { background: var(--run); }
@keyframes blip { 0%,100% { opacity: 1; } 50% { opacity: .3; } }

.fline { display: flex; align-items: baseline; justify-content: space-between; gap: 8px; margin-top: 9px; }
.fline .lbl { font-family: var(--font-mono); font-size: 9.5px; letter-spacing: .085em; text-transform: uppercase; color: var(--muted); }
.fline .val { font-family: var(--font-mono); font-size: 12px; font-variant-numeric: tabular-nums; text-align: right; }
.fline .val.hi { color: var(--accent); }
.fline .val .dim { color: var(--muted); }
.fline .val.win { color: var(--run); font-weight: 600; }

.cap { margin: 10px 0 0; font-size: 11.5px; line-height: 1.45; color: var(--muted); }
.cap b { color: var(--ink); font-weight: 600; }
.cap code { font-family: var(--font-mono); font-size: .89em; color: var(--accent); background: var(--accent-soft); border-radius: 4px; padding: 1px 4px; }

/* controls */
.ctl + .ctl { margin-top: 13px; }
.ctl .row { display: flex; align-items: baseline; justify-content: space-between; gap: 8px; margin-bottom: 5px; }
.ctl .lbl { font-family: var(--font-mono); font-size: 9.5px; letter-spacing: .085em; text-transform: uppercase; color: var(--muted); }
.ctl .val { font-family: var(--font-mono); font-size: 12.5px; color: var(--accent); font-variant-numeric: tabular-nums; }
input[type="range"] {
  -webkit-appearance: none; appearance: none; width: 100%; height: 20px;
  background: transparent; accent-color: var(--accent); cursor: pointer; margin: 0; display: block;
}
input[type="range"]:focus { outline: none; }
input[type="range"]:focus-visible { outline: 2px solid var(--accent); outline-offset: 2px; border-radius: 6px; }
input[type="range"]::-webkit-slider-runnable-track { height: 4px; border-radius: 999px; background: var(--line); }
input[type="range"]::-webkit-slider-thumb {
  -webkit-appearance: none; appearance: none; width: 15px; height: 15px; margin-top: -5.5px;
  border-radius: 50%; background: var(--accent); border: 2px solid var(--surface);
  box-shadow: 0 0 0 1px var(--accent);
}
input[type="range"]::-moz-range-track { height: 4px; border-radius: 999px; background: var(--line); }
input[type="range"]::-moz-range-thumb {
  width: 13px; height: 13px; border-radius: 50%; background: var(--accent);
  border: 2px solid var(--surface); box-shadow: 0 0 0 1px var(--accent);
}

/* buttons */
button {
  font: inherit; font-size: 13px; font-family: var(--font-sans);
  color: var(--ink); background: var(--surface);
  border: 1px solid var(--line); border-radius: 8px;
  padding: 7px 11px; cursor: pointer; line-height: 1.2;
  transition: border-color .12s ease, color .12s ease, background .12s ease;
}
button:hover:not(:disabled) { border-color: var(--accent); color: var(--accent); }
button:focus-visible { outline: 2px solid var(--accent); outline-offset: 2px; }
button:disabled { opacity: .38; cursor: not-allowed; }
button.primary { background: var(--accent); color: var(--surface); border-color: var(--accent); font-weight: 600; }
button.primary:hover:not(:disabled) { color: var(--surface); filter: brightness(1.07); }
button.primary span.m { font-family: var(--font-mono); font-variant-numeric: tabular-nums; font-size: 12px; opacity: .85; }

.balls { display: grid; grid-template-columns: repeat(2, minmax(0,1fr)); gap: 7px; margin-top: 6px; }
.balls button { display: flex; align-items: center; gap: 7px; justify-content: flex-start; font-size: 12.5px; padding: 7px 8px; text-align: left; }
.balls button .bd { border-radius: 50%; background: var(--muted); opacity: .4; flex: none; }
.balls button[aria-pressed="true"] { background: var(--accent-soft); color: var(--accent); border-color: var(--accent); font-weight: 600; }
.balls button[aria-pressed="true"] .bd { background: var(--accent); opacity: 1; }

.toggles { display: grid; grid-template-columns: repeat(2, minmax(0,1fr)); gap: 7px; margin-top: 13px; }
.toggles button { display: inline-flex; align-items: center; gap: 6px; justify-content: center; font-size: 12px; padding: 7px 6px; }
.toggles button .sw { width: 8px; height: 8px; border-radius: 50%; background: var(--muted); flex: none; opacity: .45; }
.toggles button[aria-pressed="true"] { background: var(--accent-soft); color: var(--accent); border-color: var(--accent); font-weight: 600; }
.toggles button[aria-pressed="true"] .sw { background: var(--accent); opacity: 1; }

/* shot log */
.shots { list-style: none; margin: 0; padding: 0; display: flex; flex-direction: column; gap: 5px; }
.shots li { min-width: 0; }
.shots button {
  width: 100%; display: grid; grid-template-columns: 30px minmax(0,1fr) auto; gap: 8px;
  align-items: center; padding: 6px 8px; font-family: var(--font-mono); font-size: 11.5px;
  font-variant-numeric: tabular-nums; background: var(--bg);
}
.shots button .n { color: var(--muted); font-size: 10.5px; }
.shots button .d { color: var(--muted); font-size: 10.5px; overflow: hidden; text-overflow: ellipsis; white-space: nowrap; text-align: left; }
.shots button .r { white-space: nowrap; }
.shots button.sel { border-color: var(--accent); background: var(--accent-soft); }
.shots button.sel .n, .shots button.sel .d { color: var(--accent); }
.shots button.hit .r { color: var(--run); font-weight: 600; }
.shots button:hover .d { color: inherit; }
.empty { font-family: var(--font-mono); font-size: 11px; color: var(--muted); margin: 0; }

.prose { margin: 0; font-size: 12.5px; line-height: 1.6; color: var(--muted); }
.prose + .prose { margin-top: 9px; }
.prose b { color: var(--ink); font-weight: 600; }
.prose code { font-family: var(--font-mono); font-size: .9em; color: var(--accent); }

footer { font-family: var(--font-mono); font-size: 11px; color: var(--muted); letter-spacing: .05em; padding-top: 2px; }

.sr-only { position: absolute; width: 1px; height: 1px; padding: 0; margin: -1px; overflow: hidden; clip: rect(0 0 0 0); white-space: nowrap; border: 0; }

/* one column: rebuild the reading order so the numbers follow the field */
@media (max-width: 940px) {
  .stage { display: flex; flex-direction: column; gap: 12px; align-items: stretch; }
  .left, .panel, .subgrid { display: contents; }
  .field { order: 1; } .toolbar { order: 2; }
  #cReadout { order: 3; } #cAim { order: 4; } #cBall { order: 5; } #cPaths { order: 6; } #cWhy { order: 7; }
}

@media (prefers-reduced-motion: reduce) {
  *, *::before, *::after { transition-duration: .001ms !important; animation-duration: .001ms !important; animation-iteration-count: 1 !important; }
}
</style>
</head>
<body>
<div class="wrap">

  <header>
    <h1>Projectile Playground</h1>
    <p class="lede">
      Pull the slingshot back, let go, and try to drop the ball in the bucket. The dashed line is the
      neat parabola from the textbook — the one that ignores air. The solid line is what actually
      happens once the air pushes back. <b>The gap between them is the whole story.</b>
    </p>
  </header>

  <main class="stage">

    <div class="left">
      <div class="field" id="field">
        <canvas id="sky" tabindex="0" aria-label="Launch field. A slingshot on the left, a bucket on the ground to the right, and the flight paths of your shots. Left and right arrows change the angle, up and down change the power, Enter launches.">
          A slingshot launching balls at a bucket, with flight paths drawn. Your browser does not support canvas.
        </canvas>
        <div class="grab" id="grab" aria-hidden="true"></div>
        <div class="hint" id="hint">drag the ball back to aim &mdash; or use the sliders</div>
        <div class="legend" id="legend">
          <span class="lg" id="lgAir"><span class="sw" style="border-top-color:var(--accent)"></span>with air</span>
          <span class="lg" id="lgIdeal"><span class="sw" style="border-top-style:dashed;border-top-color:var(--muted)"></span>no air</span>
        </div>
      </div>

      <div class="card toolbar" role="group" aria-label="Launch controls">
        <button type="button" class="primary" id="fireBtn">Launch <span class="m" id="fireLbl">45° · 24 m/s</span></button>
        <button type="button" id="moveBtn">Move the bucket</button>
        <button type="button" id="clearBtn">Clear paths</button>
        <span class="tbnote">Click the field, then <b>&larr; &rarr;</b> angle, <b>&uarr; &darr;</b> power, <b>Enter</b> to launch.</span>
      </div>

      <div class="subgrid">
      <section class="card" id="cPaths" aria-label="Shots so far">
        <h2>Paths kept <span class="aux" id="shotAux"></span></h2>
        <ul class="shots" id="shots"></ul>
        <p class="empty" id="shotsEmpty" hidden>no shots yet</p>
        <p class="cap">Tap a path to load its settings back into the sliders.</p>
      </section>

      <section class="card" id="cWhy" aria-label="What is going on">
        <h2>What&rsquo;s going on</h2>
        <p class="prose">
          Gravity pulls down by the same amount no matter how fast you are going. Air doesn&rsquo;t: its push
          grows with <b>speed squared</b>, so it hits hardest right after release and eases off as the ball
          slows. That is why the solid path leaves the dashed one early, then falls steeper than it rose —
          the shape stops being a parabola at all.
        </p>
        <p class="prose">
          It also moves the sweet spot. In still vacuum the farthest throw is at <code>45°</code>. Add air and
          the best angle drops — around <code>40°</code> for a tennis ball, and near <code>24°</code> for a beach
          ball, which spends so long fighting the air that a high, slow arc is simply wasted time.
        </p>
        <p class="prose">
          Try the <b>steel ball</b>: heavy, small, and so it barely notices the air. Its two paths sit almost on
          top of each other, which is exactly why the textbook version was ever a decent guess.
        </p>
      </section>
      </div>
    </div>

    <div class="panel">

      <section class="card" id="cReadout" aria-label="Flight readout">
        <h2>This shot <span class="aux" id="madeAux"></span></h2>
        <div class="tbl" id="tbl">
          <div class="th"></div><div class="th" id="thL">no air</div><div class="th hi air" id="thR">with air</div>
          <div class="rk">Distance</div><div class="rv" id="dL">&mdash;</div><div class="rv hi air" id="dR">&mdash;</div>
          <div class="rk">Peak height</div><div class="rv" id="pL">&mdash;</div><div class="rv hi air" id="pR">&mdash;</div>
          <div class="rk">Time in air</div><div class="rv" id="tL">&mdash;</div><div class="rv hi air" id="tR">&mdash;</div>
          <div class="rk">Landing speed</div><div class="rv" id="vL">&mdash;</div><div class="rv hi air" id="vR">&mdash;</div>
        </div>
        <span class="pill" id="pill" role="status"><span class="dot"></span><span id="pillText">loaded &mdash; ready to launch</span></span>
        <div class="fline"><span class="lbl">Bucket sits at</span><span class="val" id="fBucket">&mdash;</span></div>
        <div class="fline"><span class="lbl">Best angle now</span><span class="val hi" id="fBest">&mdash;</span></div>
        <p class="cap" id="fCost">Air is taking a bite out of this shot.</p>
      </section>

      <section class="card" id="cAim" aria-label="Aim">
        <h2>Aim</h2>

        <div class="ctl">
          <div class="row"><label class="lbl" for="angle">Angle</label><span class="val" id="vAngle">45°</span></div>
          <input type="range" id="angle" min="5" max="85" step="1" value="45">
        </div>

        <div class="ctl">
          <div class="row"><label class="lbl" for="power">Power</label><span class="val" id="vPower">24.0 m/s</span></div>
          <input type="range" id="power" min="8" max="34" step="0.5" value="24">
        </div>

        <div class="ctl">
          <div class="row"><label class="lbl" for="dist">Bucket at</label><span class="val" id="vDist">38 m</span></div>
          <input type="range" id="dist" min="4" max="95" step="1" value="38">
        </div>

        <div class="toggles" role="group" aria-label="Options">
          <button type="button" id="airBtn" aria-pressed="true"><span class="sw" aria-hidden="true"></span>Air is on</button>
          <button type="button" id="ghostBtn" aria-pressed="true"><span class="sw" aria-hidden="true"></span>Keep paths</button>
        </div>
      </section>

      <section class="card" id="cBall" aria-label="Ball">
        <h2>Ball</h2>
        <div class="balls" id="balls" role="group" aria-label="Pick a ball"></div>
        <div class="fline"><span class="lbl">Weight &amp; size</span><span class="val" id="fBall">&mdash;</span></div>
        <div class="fline"><span class="lbl">Drag factor</span><span class="val hi" id="fK">&mdash;</span></div>
        <p class="cap">Drag factor is <code>½·ρ·C·A ÷ m</code> — how much air the ball has to shove aside for every gram it carries. A beach ball is nearly all sail and no mass.</p>
      </section>

    </div>
  </main>

  <footer>demo · sloprun.dev</footer>
</div>
<p class="sr-only" id="live" aria-live="polite"></p>

<script>
(function () {
  "use strict";

  /* ── theme + motion plumbing ────────────────────────────────────────────── */
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  var mqDark = window.matchMedia ? matchMedia("(prefers-color-scheme: dark)") : null;
  var mqRM   = window.matchMedia ? matchMedia("(prefers-reduced-motion: reduce)") : null;
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  /* ── elements ───────────────────────────────────────────────────────────── */
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      'font-size:12px;line-height:1.6;color:var(--danger)" role="alert">Canvas is not available in ' +
      'this browser, so the flight paths can&rsquo;t be drawn. Every part of this demo needs it.</p>';
    var dead = document.querySelectorAll(".wrap button, .wrap input"), di;
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  /* ── physics constants ──────────────────────────────────────────────────── */
  var G = 9.81;          /* m/s²                                             */
  var H0 = 1.2;          /* release height of the pouch, metres              */
  var HALF = 1.25;       /* half-width of the bucket mouth, metres           */
  var DT = 0.004;        /* integrator step, seconds                         */

  var BALLS = [
    { name: "Beach ball",  k: 0.3630,  m: 100,  d: 40,   r: 9 },
    { name: "Tennis ball", k: 0.01806, m: 58,   d: 6.6,  r: 5 },
    { name: "Baseball",    k: 0.00622, m: 145,  d: 7.3,  r: 5.5 },
    { name: "Steel ball",  k: 0.00082, m: 1000, d: 6.0,  r: 4.5 }
  ];

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  function grn(a) { return "rgba(" + runRGB[0] + "," + runRGB[1] + "," + runRGB[2] + "," + a + ")"; }
  function mut(a) { return "rgba(" + mutRGB[0] + "," + mutRGB[1] + "," + mutRGB[2] + "," + a + ")"; }

  /* ── helpers ────────────────────────────────────────────────────────────── */
  function clamp(v, a, b) { return v < a ? a : (v > b ? b : v); }
  function fx(n, d) { return (Math.round(n * Math.pow(10, d)) / Math.pow(10, d)).toFixed(d); }
  function setTxt(el, t) { if (el && el.textContent !== t) el.textContent = t; }
  function say(t) { if (live.textContent !== t) live.textContent = t; }

  /* ── state ──────────────────────────────────────────────────────────────── */
  var S = {
    angle: 45, power: 24, dist: 38, ball: 1,
    air: true, keep: true,
    made: 0, fired: 0, sel: -1
  };
  var trails = [];         /* kept paths                                     */
  var flight = null;       /* the ball currently in the air                  */
  var sparks = [];         /* celebration bits                               */
  var lastResult = null;   /* the shot that just landed                      */
  var bucketHot = false;   /* the bucket stays green until the next launch   */
  var bucketGlow = 0;      /* 1 → 0 flare on top of that                     */

  /* ── the maths ──────────────────────────────────────────────────────────── */

  /* No air: closed form, launched from H0. */
  function idealShot(v, angDeg) {
    var th = angDeg * Math.PI / 180, vx = v * Math.cos(th), vy = v * Math.sin(th);
    var t = (vy + Math.sqrt(vy * vy + 2 * G * H0)) / G;
    var n = 140, xs = new Float64Array(n + 1), ys = new Float64Array(n + 1), ts = new Float64Array(n + 1), i, tt;
    for (i = 0; i <= n; i++) {
      tt = t * i / n;
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    }
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      xs: xs, ys: ys, ts: ts, n: n + 1,
      range: vx * t, peak: H0 + vy * vy / (2 * G), time: t,
      vimp: Math.sqrt(vx * vx + (vy - G * t) * (vy - G * t))
    };
  }

  /* With air: quadratic drag, a = -k|v|v, integrated with RK4. */
  function deriv(s, k, out) {
    var sp = Math.sqrt(s[2] * s[2] + s[3] * s[3]);
    out[0] = s[2]; out[1] = s[3];
    out[2] = -k * sp * s[2];
    out[3] = -G - k * sp * s[3];
  }
  var _a = [0,0,0,0], _b = [0,0,0,0], _c = [0,0,0,0], _e = [0,0,0,0], _t = [0,0,0,0];
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    deriv(_t, k, _b);
    for (j = 0; j < 4; j++) _t[j] = s[j] + dt / 2 * _b[j];
    deriv(_t, k, _c);
    for (j = 0; j < 4; j++) _t[j] = s[j] + dt * _c[j];
    deriv(_t, k, _e);
    for (j = 0; j < 4; j++) s[j] += dt / 6 * (_a[j] + 2 * _b[j] + 2 * _c[j] + _e[j]);
  }

  function dragShot(v, angDeg, k, wantPath) {
    var th = angDeg * Math.PI / 180;
    var s = [0, H0, v * Math.cos(th), v * Math.sin(th)];
    var px = 0, py = H0, pvx = s[2], pvy = s[3];
    var t = 0, peak = H0, i, f, MAXI = 12000;
    var xs = [], ys = [], ts = [], keepEvery = 2;
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    for (i = 1; i <= MAXI; i++) {
      px = s[0]; py = s[1]; pvx = s[2]; pvy = s[3];
      stepRK4(s, k, DT);
      t += DT;
      if (s[1] > peak) peak = s[1];
      if (s[1] <= 0) {
        f = (py - s[1]) !== 0 ? py / (py - s[1]) : 0;
        var lx = px + f * (s[0] - px), lt = t - DT + f * DT;
        if (wantPath) { xs.push(lx); ys.push(0); ts.push(lt); }
        return {
          xs: xs, ys: ys, ts: ts, n: xs.length,
          range: lx, peak: peak, time: lt,
          vimp: Math.sqrt(pvx * pvx + pvy * pvy)
        };
      }
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    }
    return { xs: xs, ys: ys, ts: ts, n: xs.length, range: s[0], peak: peak, time: t,
             vimp: Math.sqrt(s[2] * s[2] + s[3] * s[3]) };
  }

  function dragRange(v, angDeg, k) { return dragShot(v, angDeg, k, false).range; }

  /* Angle that throws farthest, given the current ball. */
  function bestAngleAir(v, k) {
    var best = 45, br = -1, a, r;
    for (a = 6; a <= 84; a += 2) { r = dragRange(v, a, k); if (r > br) { br = r; best = a; } }
    for (a = best - 2; a <= best + 2; a += 0.5) {
      if (a < 5 || a > 85) continue;
      r = dragRange(v, a, k); if (r > br) { br = r; best = a; }
    }
    return { angle: best, range: br };
  }
  /* Farthest this ball can go at all — used to keep the bucket reachable.
     A beach ball tops out near 7 m, so parking the bucket at 38 m would make
     the whole game unwinnable the moment you picked it. */
  function maxReach(bi) {
    var b = BALLS[bi];
    if (b._reach === undefined) b._reach = bestAngleAir(+powerIn.max, b.k).range;
    return b._reach;
  }
  function bestAngleIdeal(v) {
    /* launching from height H0 the optimum dips just under 45° */
    var s = 1 / Math.sqrt(2 + 2 * G * H0 / (v * v));
    return Math.asin(clamp(s, 0, 1)) * 180 / Math.PI;
  }

  /* ── derived, cached per settings change ────────────────────────────────── */
  var cur = { ideal: null, air: null, best: null, bestKey: "" };

  function recompute() {
    var k = BALLS[S.ball].k;
    cur.ideal = idealShot(S.power, S.angle);
    cur.air = S.air ? dragShot(S.power, S.angle, k, true) : null;
    var key = S.power + "|" + S.ball + "|" + (S.air ? 1 : 0);
    if (key !== cur.bestKey) {
      cur.bestKey = key;
      cur.best = S.air ? bestAngleAir(S.power, k) : { angle: bestAngleIdeal(S.power), range: idealShot(S.power, bestAngleIdeal(S.power)).range };
    }
  }

  function realShot() { return S.air ? cur.air : cur.ideal; }

  /* ── canvas sizing ──────────────────────────────────────────────────────── */
  var CW = 0, CH = 0, DPR = 1, measured = false;
  function resize() {
    var r = field.getBoundingClientRect();
    var w = Math.round(r.width), h = Math.round(r.height);
    /* A hidden or not-yet-flowed box measures ~0. Taking that as real would latch
       a tight layout and a 4× wrong scale for the rest of the session, and nothing
       recomputes the fitted height afterwards — so wait for a real measurement. */
    if (w < 60 || h < 60) { measured = false; return; }
    if (!measured) scale = 0;         /* first real size: snap, don't ease from junk */
    measured = true;
    DPR = Math.min(window.devicePixelRatio || 1, 2);
    CW = w;
    CH = h;
    var tight = CW < 640;
    PADL = tight ? 30 : 40; PADR = tight ? 14 : 20;
    PADT = tight ? 16 : 24; PADB = tight ? 36 : 42;
    var pw = Math.round(CW * DPR), ph = Math.round(CH * DPR);
    /* assigning width/height wipes the bitmap, so only do it when it really moved */
    if (cv.width !== pw || cv.height !== ph) { cv.width = pw; cv.height = ph; }
    requestFrame();
  }

  /* ── world → pixel mapping (uniform scale, so the arcs stay honest) ─────── */
  var PADL = 40, PADR = 20, PADT = 24, PADB = 42;
  var scale = 0, scaleTarget = 0, originX = 0, originY = 0, viewTop = 20;

  function computeScale() {
    var maxX = Math.max(S.dist + 4, 16), maxY = 5, i;
    var a = cur.ideal, b = cur.air;
    if (a) { maxX = Math.max(maxX, a.range); maxY = Math.max(maxY, a.peak); }
    if (b) { maxX = Math.max(maxX, b.range); maxY = Math.max(maxY, b.peak); }
    if (flight) { maxX = Math.max(maxX, flight.path.range); maxY = Math.max(maxY, flight.path.peak); }
    for (i = 0; i < trails.length; i++) { maxX = Math.max(maxX, trails[i].range); maxY = Math.max(maxY, trails[i].peak); }
    /* quantise so tiny slider moves don't jiggle the whole view */
    var wW = Math.ceil(maxX * 1.07 / 5) * 5;
    var wH = Math.ceil(maxY * 1.20 / 2) * 2;
    var availW = Math.max(40, CW - PADL - PADR), availH = Math.max(40, CH - PADT - PADB);
    scaleTarget = Math.min(availW / wW, availH / wH);
    viewTop = wH;   /* stop the height ruler where the flight stops — the rest reads as sky */
    lastWW = wW; lastWH = wH;
    if (scale === 0) scale = scaleTarget;
    originX = PADL;
    originY = CH - PADB;
  }

  /* A throw is a wide, flat thing. Let the field box take the shape the flight
     actually needs instead of leaving two thirds of it as empty sky. Only ever
     called when nothing is mid-gesture, so controls never move under a finger. */
  var lastWW = 0, lastWH = 0;
  function fitHeight() {
    if (!measured || flight || aiming) return;
    computeScale();
    var availW = Math.max(40, CW - PADL - PADR);
    var want = lastWH * (availW / lastWW) + PADT + PADB;
    var narrow = CW < 640;
    var minH = narrow ? 205 : 285;
    var maxH = Math.max(minH, Math.min(narrow ? 400 : 500, (window.innerHeight || 800) - 260));
    want = Math.round(clamp(want, minH, maxH) / 8) * 8;
    if (Math.abs(want - CH) <= 16) return;
    field.style.height = want + "px";
    if (!window.ResizeObserver) setTimeout(resize, 260);
  }
  function px(x) { return originX + x * scale; }
  function py(y) { return originY - y * scale; }

  /* ── drawing ────────────────────────────────────────────────────────────── */
  function tickStep(spanM) {
    var cands = [1, 2, 5, 10, 20, 25, 50, 100], i;
    for (i = 0; i < cands.length; i++) if (spanM / cands[i] <= 9) return cands[i];
    return 200;
  }

  function drawPath(p, from, to) {
    var i, started = false;
    ctx.beginPath();
    for (i = from; i <= to && i < p.n; i++) {
      if (!started) { ctx.moveTo(px(p.xs[i]), py(p.ys[i])); started = true; }
      else ctx.lineTo(px(p.xs[i]), py(p.ys[i]));
    }
    ctx.stroke();
  }

  /* The slingshot: frame at x = 0, ball resting at the release height. While the
     visitor drags, the ball follows the pointer and the bands stretch to it. */
  function drawSling(aimAng, pullFrac, pouchX, pouchY) {
    var bx = px(0), gy = py(0), by = py(H0);
    var topY = Math.min(by - 7, gy - 34);          /* prong tips, always legible */
    var forkY = topY + (gy - topY) * 0.46;
    /* at rest the pouch sits drawn back along the aim, further for more power */
    var th = aimAng * Math.PI / 180, pull = 7 + pullFrac * 25;
    var ox = pouchX === null ? bx - Math.cos(th) * pull : pouchX;
    var oy = pouchY === null ? Math.min(gy - 4, by + Math.sin(th) * pull) : pouchY;

    ctx.lineCap = "round"; ctx.lineJoin = "round";
    ctx.strokeStyle = ink(0.5); ctx.lineWidth = 2.8;
    ctx.beginPath(); ctx.moveTo(bx, gy); ctx.lineTo(bx, forkY); ctx.stroke();
    ctx.lineWidth = 2.2;
    ctx.beginPath();
    ctx.moveTo(bx, forkY); ctx.lineTo(bx - 7, topY);
    ctx.moveTo(bx, forkY); ctx.lineTo(bx + 7, topY);
    ctx.stroke();

    /* bands */
    ctx.strokeStyle = acc(0.7); ctx.lineWidth = 1.5;
    ctx.beginPath();
    ctx.moveTo(bx - 7, topY); ctx.lineTo(ox, oy); ctx.lineTo(bx + 7, topY);
    ctx.stroke();

    /* the angle, drawn as an angle */
    ctx.strokeStyle = ink(0.2); ctx.lineWidth = 1;
    ctx.beginPath(); ctx.moveTo(bx, by); ctx.lineTo(bx + 20, by); ctx.stroke();
    ctx.beginPath(); ctx.arc(bx, by, 16, -th, 0); ctx.stroke();

    return { x: ox, y: oy, bx: bx, by: by };
  }

  function drawBall(x, y, r, fill) {
    ctx.beginPath(); ctx.arc(x, y, r, 0, Math.PI * 2);
    ctx.fillStyle = fill; ctx.fill();
    ctx.lineWidth = 1; ctx.strokeStyle = COL.surface; ctx.stroke();
  }

  function drawBucket() {
    var cx = px(S.dist), gy = py(0);
    var w = Math.max(9, HALF * scale);          /* half-width in px          */
    var h = Math.min(26, Math.max(12, w * 0.9));
    var hot = bucketHot;
    var stroke = hot ? grn(0.9) : ink(0.5);
    var fill = hot ? grn(0.18 + 0.3 * bucketGlow) : ink(0.05);

    /* guide line so a far bucket is still findable */
    ctx.save();
    ctx.setLineDash([2, 5]); ctx.lineWidth = 1;
    ctx.strokeStyle = hot ? grn(0.45) : ink(0.16);
    ctx.beginPath(); ctx.moveTo(cx, gy - h); ctx.lineTo(cx, gy - h - 34); ctx.stroke();
    ctx.restore();

    /* the bucket: a tapered tub sitting on the ground */
    ctx.beginPath();
    ctx.moveTo(cx - w, gy - h);
    ctx.lineTo(cx - w * 0.66, gy);
    ctx.lineTo(cx + w * 0.66, gy);
    ctx.lineTo(cx + w, gy - h);
    ctx.closePath();
    ctx.fillStyle = fill; ctx.fill();
    ctx.lineWidth = 1.8; ctx.strokeStyle = stroke; ctx.stroke();
    /* rim */
    ctx.beginPath(); ctx.moveTo(cx - w - 1.5, gy - h); ctx.lineTo(cx + w + 1.5, gy - h);
    ctx.lineWidth = 2.4; ctx.strokeStyle = stroke; ctx.stroke();

    /* label */
    ctx.font = "600 10px " + MONO;
    ctx.textAlign = "center"; ctx.textBaseline = "bottom";
    ctx.fillStyle = hot ? grn(1) : mut(1);
    ctx.fillText(hot ? "IN!" : S.dist + " m", cx, gy - h - 38);
  }

  function drawGround() {
    var gy = py(0);
    ctx.fillStyle = ink(0.035);
    ctx.fillRect(0, gy, CW, CH - gy);
    ctx.strokeStyle = ink(0.42); ctx.lineWidth = 1.4;
    ctx.beginPath(); ctx.moveTo(0, gy + 0.5); ctx.lineTo(CW, gy + 0.5); ctx.stroke();

    var spanX = (CW - PADL - PADR) / scale, step = tickStep(spanX), i, x;
    ctx.font = "9.5px " + MONO; ctx.textAlign = "center"; ctx.textBaseline = "top";
    for (i = step; i * scale + PADL < CW - 4; i += step) {
      x = px(i);
      ctx.strokeStyle = ink(0.2); ctx.lineWidth = 1;
      ctx.beginPath(); ctx.moveTo(x, gy); ctx.lineTo(x, gy + 5); ctx.stroke();
      ctx.fillStyle = mut(0.95);
      ctx.fillText(String(i), x, gy + 6);
    }
    ctx.textAlign = "right"; ctx.fillStyle = mut(0.8);
    ctx.fillText("m", PADL - 9, gy + 6);

    /* height ruler */
    var spanY = Math.min((CH - PADT - PADB) / scale, viewTop), stepY = tickStep(spanY), j, y;
    ctx.textAlign = "right"; ctx.textBaseline = "middle";
    for (j = stepY; j <= spanY + 0.01; j += stepY) {
      y = py(j);
      ctx.strokeStyle = ink(0.09); ctx.lineWidth = 1;
      ctx.beginPath(); ctx.moveTo(PADL - 6, y + 0.5); ctx.lineTo(CW - 2, y + 0.5); ctx.stroke();
      ctx.fillStyle = mut(0.9);
      ctx.fillText(String(j), PADL - 9, y);
    }
  }

  function drawApex(p, colour) {
    var i, bi = 0, best = -1;
    for (i = 0; i < p.n; i++) if (p.ys[i] > best) { best = p.ys[i]; bi = i; }
    var x = px(p.xs[bi]), y = py(p.ys[bi]);
    ctx.save();
    ctx.setLineDash([2, 4]); ctx.lineWidth = 1; ctx.strokeStyle = colour(0.3);
    ctx.beginPath(); ctx.moveTo(x, y); ctx.lineTo(x, py(0)); ctx.stroke();
    ctx.restore();
    ctx.beginPath(); ctx.arc(x, y, 2.5, 0, Math.PI * 2); ctx.fillStyle = colour(0.75); ctx.fill();
    ctx.font = "9.5px " + MONO; ctx.textAlign = "center"; ctx.textBaseline = "bottom";
    ctx.fillStyle = colour(0.85);
    ctx.fillText(fx(best, 1) + " m", x, y - 6);
  }

  function drawLandMark(p, colour, label, dash) {
    var x = px(p.range), gy = py(0);
    ctx.save();
    if (dash) ctx.setLineDash([2, 3]);
    ctx.strokeStyle = colour(0.55); ctx.lineWidth = 1.4;
    ctx.beginPath(); ctx.moveTo(x, gy - 6); ctx.lineTo(x, gy + 6); ctx.stroke();
    ctx.restore();
    if (label) {
      ctx.font = "9.5px " + MONO; ctx.textAlign = "center"; ctx.textBaseline = "top";
      ctx.fillStyle = colour(0.8);
      ctx.fillText(fx(p.range, 1) + " m", x, gy + 19);
    }
  }

  function draw() {
    ctx.setTransform(DPR, 0, 0, DPR, 0, 0);
    ctx.clearRect(0, 0, CW, CH);
    ctx.fillStyle = COL.surface; ctx.fillRect(0, 0, CW, CH);
    ctx.lineCap = "round"; ctx.lineJoin = "round";

    drawGround();
    drawBucket();

    /* kept paths from earlier shots */
    var i, tr;
    for (i = 0; i < trails.length; i++) {
      tr = trails[i];
      var isSel = (S.sel === tr.id);
      ctx.strokeStyle = isSel ? acc(0.6) : (tr.hit ? grn(0.55) : mut(0.5));
      ctx.lineWidth = isSel ? 2 : 1.2;
      drawPath(tr.path, 0, tr.path.n - 1);
      ctx.beginPath(); ctx.arc(px(tr.range), py(0), isSel ? 3.2 : 2.2, 0, Math.PI * 2);
      ctx.fillStyle = isSel ? acc(0.8) : (tr.hit ? grn(0.8) : mut(0.7)); ctx.fill();
    }

    var real = realShot();

    /* the no-air ghost */
    if (S.air && cur.ideal) {
      ctx.save();
      ctx.setLineDash([5, 5]);
      ctx.strokeStyle = mut(0.9); ctx.lineWidth = 1.5;
      drawPath(cur.ideal, 0, cur.ideal.n - 1);
      ctx.restore();
      var apart = Math.abs(cur.ideal.range - real.range) * scale;
      drawLandMark(cur.ideal, mut, apart > 40, true);
    }

    /* the path the ball will actually take */
    if (real) {
      ctx.strokeStyle = acc(0.95); ctx.lineWidth = 2.2;
      drawPath(real, 0, real.n - 1);
      drawApex(real, acc);
      drawLandMark(real, acc, true, false);
    }

    /* live ball */
    if (flight) {
      var pt = sampleAt(flight.path, flight.t);
      drawBall(px(pt.x), py(pt.y), BALLS[flight.ball].r, COL.accent);
    }

    /* celebration bits */
    for (i = 0; i < sparks.length; i++) {
      var sp = sparks[i];
      ctx.globalAlpha = clamp(sp.life, 0, 1);
      ctx.beginPath(); ctx.arc(px(sp.x), py(sp.y), sp.r, 0, Math.PI * 2);
      ctx.fillStyle = COL.run; ctx.fill();
      ctx.globalAlpha = 1;
    }

    /* slingshot last, so it sits on top */
    var pouch = drawSling(S.angle, (S.power - 8) / 26,
                          aiming && aimMoved ? aimPx : null, aiming && aimMoved ? aimPy : null);
    if (!flight) {
      if (!hintGone) {   /* a grab-me ring until the visitor has touched anything */
        ctx.save();
        ctx.setLineDash([3, 4]); ctx.lineWidth = 1.2; ctx.strokeStyle = acc(0.5);
        ctx.beginPath(); ctx.arc(pouch.x, pouch.y, BALLS[S.ball].r + 7, 0, Math.PI * 2); ctx.stroke();
        ctx.restore();
      }
      drawBall(pouch.x, pouch.y, BALLS[S.ball].r, COL.accent);
    }

    if (aiming && aimMoved) {
      ctx.font = "600 11px " + MONO; ctx.textAlign = "left"; ctx.textBaseline = "middle";
      ctx.fillStyle = COL.accent;
      ctx.fillText(S.angle + "° · " + fx(S.power, 1) + " m/s", pouch.x - 4, pouch.y - 22);
    }

    positionGrab();
  }

  function sampleAt(p, t) {
    var lo = 0, hi = p.n - 1, mid;
    if (t <= 0) return { x: p.xs[0], y: p.ys[0] };
    if (t >= p.ts[hi]) return { x: p.xs[hi], y: p.ys[hi] };
    while (hi - lo > 1) { mid = (lo + hi) >> 1; if (p.ts[mid] <= t) lo = mid; else hi = mid; }
    var span = p.ts[hi] - p.ts[lo], f = span > 0 ? (t - p.ts[lo]) / span : 0;
    return { x: p.xs[lo] + f * (p.xs[hi] - p.xs[lo]), y: p.ys[lo] + f * (p.ys[hi] - p.ys[lo]) };
  }

  /* ── animation loop ─────────────────────────────────────────────────────── */
  var raf = 0, lastTs = 0;
  function requestFrame() { if (ctx && !raf) raf = requestAnimationFrame(frame); }
  function busy() {
    return !!flight || sparks.length > 0 || bucketGlow > 0.01 ||
           Math.abs(scale - scaleTarget) > scaleTarget * 0.0025;
  }
  function frame(ts) {
    raf = 0;
    var dt = lastTs ? Math.min(0.05, (ts - lastTs) / 1000) : 0.016;
    lastTs = ts;

    computeScale();
    if (reduced()) scale = scaleTarget;
    else scale += (scaleTarget - scale) * Math.min(1, dt * 9);

    if (flight) {
      flight.t += dt;
      if (flight.t >= flight.path.time) { flight.t = flight.path.time; land(); }
    }
    var i;
    for (i = sparks.length - 1; i >= 0; i--) {
      var s = sparks[i];
      s.vy -= G * dt; s.x += s.vx * dt; s.y += s.vy * dt; s.life -= dt * 1.25;
      if (s.life <= 0 || s.y < 0) sparks.splice(i, 1);
    }
    if (bucketGlow > 0) bucketGlow = Math.max(0, bucketGlow - dt * 0.9);

    draw();
    if (busy()) requestFrame();
  }

  /* ── launching ──────────────────────────────────────────────────────────── */
  function launch(auto) {
    if (flight) return;
    recompute();
    var path = realShot();
    if (!path) return;
    S.fired++;
    var rec = {
      id: S.fired, angle: S.angle, power: S.power, ball: S.ball, air: S.air,
      path: path, range: path.range, peak: path.peak, time: path.time, vimp: path.vimp, hit: false
    };
    var off = path.range - S.dist;
    rec.hit = Math.abs(off) <= HALF;
    rec.off = off;

    flight = { path: path, t: 0, ball: S.ball, rec: rec };
    bucketHot = false; bucketGlow = 0;
    setPill("busy", "in the air…");
    fireBtn.disabled = true;
    if (!auto) hideHint();
    if (reduced()) { flight.t = path.time; land(); }
    requestFrame();
  }

  function land() {
    var rec = flight.rec;
    flight = null;
    lastResult = rec;
    fireBtn.disabled = false;

    if (rec.hit) {
      S.made++;
      bucketHot = true;
      bucketGlow = reduced() ? 0 : 1;
      if (!reduced()) {
        var i, a, sp;
        for (i = 0; i < 16; i++) {
          a = (-0.15 - Math.random() * 0.7) * Math.PI;
          sp = 3 + Math.random() * 6;
          sparks.push({ x: S.dist + (Math.random() - 0.5) * 1.5, y: 0.9,
                        vx: Math.cos(a) * sp * (Math.random() < 0.5 ? -1 : 1) * 0.6,
                        vy: Math.abs(Math.sin(a)) * sp, r: 1.5 + Math.random() * 1.6, life: 1 });
        }
      }
      setPill("ok", "in the bucket — " + fx(Math.abs(rec.off), 2) + " m off centre");
      say("In the bucket. Landed at " + fx(rec.range, 1) + " metres, " + fx(Math.abs(rec.off), 2) + " metres from the centre.");
    } else {
      var word = rec.off < 0 ? "short by " : "long by ";
      setPill("", word + fx(Math.abs(rec.off), 1) + " m");
      say("Landed at " + fx(rec.range, 1) + " metres, " + word + fx(Math.abs(rec.off), 1) + " metres.");
    }

    if (S.keep) {
      trails.push(rec);
      if (trails.length > 6) trails.shift();
    }
    S.sel = -1;
    renderShots();
    updateReadout();
    fitHeight();
    requestFrame();
  }

  function setPill(cls, text) {
    pill.className = "pill" + (cls ? " " + cls : "");
    setTxt(pillText, text);
  }

  /* ── panel rendering ────────────────────────────────────────────────────── */
  function unit(v, d, u) { return fx(v, d) + '<span class="u">' + u + "</span>"; }
  function setHTML(el, h) { if (el.innerHTML !== h) el.innerHTML = h; }

  function updateReadout() {
    var a = cur.ideal, b = cur.air;
    if (S.air) {
      tbl.classList.remove("solo");
      setTxt(thL, "no air"); setTxt(thR, "with air");
      setHTML(dL, unit(a.range, 1, "m"));  setHTML(dR, unit(b.range, 1, "m"));
      setHTML(pL, unit(a.peak, 1, "m"));   setHTML(pR, unit(b.peak, 1, "m"));
      setHTML(tL, unit(a.time, 2, "s"));   setHTML(tR, unit(b.time, 2, "s"));
      setHTML(vL, unit(a.vimp, 1, "m/s")); setHTML(vR, unit(b.vimp, 1, "m/s"));
      var lost = a.range - b.range, pct = a.range > 0 ? lost / a.range * 100 : 0;
      fCost.innerHTML = "Air is eating <b>" + fx(lost, 1) + " m</b> of this throw — " +
        fx(pct, 0) + "% of the distance the textbook parabola promised.";
    } else {
      tbl.classList.add("solo");
      setTxt(thL, "this shot");
      setHTML(dL, unit(a.range, 1, "m"));
      setHTML(pL, unit(a.peak, 1, "m"));
      setHTML(tL, unit(a.time, 2, "s"));
      setHTML(vL, unit(a.vimp, 1, "m/s"));
      fCost.innerHTML = "Air is <b>off</b> — this is the clean parabola, the same curve every physics book draws.";
    }

    var real = realShot();
    var gap = real.range - S.dist;
    fBucket.innerHTML = S.dist + " m &middot; <span class=\"dim\">" +
      (Math.abs(gap) <= HALF ? "in reach" : (gap < 0 ? fx(-gap, 1) + " m short" : fx(gap, 1) + " m long")) + "</span>";

    var bi = bestAngleIdeal(S.power);
    if (S.air) {
      fBest.innerHTML = fx(cur.best.angle, 0) + "° <span class=\"dim\">&middot; " + fx(bi, 0) + "° with no air</span>";
    } else {
      /* one decimal here: launching from 1.2 m shaves a fraction off 45°, and
         rounding it away would print "45° · 45°" and look like a bug */
      fBest.innerHTML = fx(bi, 1) + "° <span class=\"dim\">&middot; 45° from ground level</span>";
    }

    if (S.made > 0) {
      madeAux.innerHTML = '<span style="color:var(--run);font-weight:600">' + S.made + " in the bucket</span>";
    } else { madeAux.textContent = ""; }

    setTxt(vAngle, S.angle + "°");
    setTxt(vPower, fx(S.power, 1) + " m/s");
    setTxt(vDist, S.dist + " m");
    setTxt(fireLbl, S.angle + "° · " + fx(S.power, 1) + " m/s");

    var bl = BALLS[S.ball];
    fBall.textContent = (bl.m >= 1000 ? "1.0 kg" : bl.m + " g") + " · " + fx(bl.d, bl.d < 10 ? 1 : 0) + " cm across";
    fK.textContent = bl.k.toFixed(5).replace(/0+$/, "") + " /m";

    /* with air off the solid line IS the no-air path — relabel, don't lie */
    lgIdeal.className = "lg" + (S.air ? "" : " off");
    lgAir.className = "lg";
    lgAir.lastChild.nodeValue = S.air ? "with air" : "no air";
  }

  function renderShots() {
    shotAux.textContent = trails.length ? trails.length + "/6" : "";
    shotsEmpty.hidden = trails.length > 0;
    clearBtn.disabled = trails.length === 0;
    var html = "", i, t, nm;
    for (i = trails.length - 1; i >= 0; i--) {
      t = trails[i];
      nm = BALLS[t.ball].name.split(" ")[0].toLowerCase();
      html += '<li><button type="button" class="' + (t.hit ? "hit " : "") + (S.sel === t.id ? "sel" : "") +
        '" data-id="' + t.id + '">' +
        '<span class="n">#' + t.id + '</span>' +
        '<span class="d">' + t.angle + "° · " + fx(t.power, 0) + " m/s · " + nm + (t.air ? "" : " · no air") + "</span>" +
        '<span class="r">' + fx(t.range, 1) + " m" + (t.hit ? " ✓" : "") + "</span>" +
        "</button></li>";
    }
    shotsUl.innerHTML = html;
  }

  function renderBalls() {
    var html = "", i, b;
    for (i = 0; i < BALLS.length; i++) {
      b = BALLS[i];
      var dia = Math.max(7, Math.min(15, 6 + Math.sqrt(b.d) * 1.5));
      html += '<button type="button" data-i="' + i + '" aria-pressed="' + (S.ball === i) + '">' +
        '<span class="bd" style="width:' + dia + "px;height:" + dia + 'px"></span>' + b.name + "</button>";
    }
    ballsBox.innerHTML = html;
  }

  /* ── interaction ────────────────────────────────────────────────────────── */
  var hintGone = false;
  function hideHint() { if (!hintGone) { hintGone = true; hint.classList.add("gone"); } }

  /* held arrow keys fire ~30×/s; refitting the box on each one would shudder */
  var refitTimer = 0;
  function refitSoon() {
    if (refitTimer) clearTimeout(refitTimer);
    refitTimer = setTimeout(function () { refitTimer = 0; fitHeight(); }, 180);
  }

  function changed(announce, refit) {
    recompute();
    updateReadout();
    positionGrab();
    if (refit) fitHeight();
    requestFrame();
    if (announce) say(announce);
  }

  angleIn.addEventListener("input", function () {
    S.angle = +angleIn.value; if (!flight) setPill("", "aim changed — ready"); changed();
  });
  powerIn.addEventListener("input", function () {
    S.power = +powerIn.value; if (!flight) setPill("", "aim changed — ready"); changed();
  });
  distIn.addEventListener("input", function () {
    S.dist = +distIn.value; bucketHot = false; bucketGlow = 0; changed();
  });
  [angleIn, powerIn, distIn].forEach(function (el) {
    el.addEventListener("change", function () { fitHeight(); });
  });

  airBtn.addEventListener("click", function () {
    S.air = !S.air;
    airBtn.setAttribute("aria-pressed", String(S.air));
    airBtn.lastChild.nodeValue = S.air ? "Air is on" : "Air is off";
    changed(S.air ? "Air resistance on." : "Air resistance off — clean parabola.", true);
  });
  ghostBtn.addEventListener("click", function () {
    S.keep = !S.keep;
    ghostBtn.setAttribute("aria-pressed", String(S.keep));
    ghostBtn.lastChild.nodeValue = S.keep ? "Keep paths" : "Drop paths";
    if (!S.keep) { trails.length = 0; S.sel = -1; renderShots(); }
    changed(S.keep ? "Paths will be kept." : "Paths cleared.", true);
  });

  ballsBox.addEventListener("click", function (e) {
    var b = e.target.closest ? e.target.closest("button[data-i]") : null;
    if (!b) return;
    S.ball = +b.getAttribute("data-i");
    var kids = ballsBox.querySelectorAll("button"), i;
    for (i = 0; i < kids.length; i++) kids[i].setAttribute("aria-pressed", String(i === S.ball));
    /* keep the bucket somewhere this ball can actually reach */
    var reach = maxReach(S.ball), note = "";
    if (S.dist > reach + HALF) {
      S.dist = clamp(Math.round(reach * 0.7), +distIn.min, +distIn.max);
      distIn.value = String(S.dist);
      bucketHot = false; bucketGlow = 0;
      note = " Bucket pulled in to " + S.dist + " metres — that is all this ball can throw.";
      setPill("", "bucket moved to " + S.dist + " m — " + BALLS[S.ball].name.toLowerCase() + " can't throw further");
    }
    changed(BALLS[S.ball].name + " selected." + note, true);
  });

  fireBtn.addEventListener("click", function () { launch(); });

  moveBtn.addEventListener("click", function () {
    var DMIN = +distIn.min, DMAX = +distIn.max;
    var now = realShot() ? realShot().range : 40;
    var cap = Math.min(DMAX, maxReach(S.ball));      /* never park it out of reach */
    var lo = Math.max(DMIN, Math.round(now * 0.45));
    var hi = Math.min(cap, Math.round(now * 1.35) + 6);
    if (hi <= lo) { lo = DMIN; hi = Math.max(DMIN + 1, Math.round(cap)); }
    var d = Math.round(lo + Math.random() * (hi - lo));
    if (d === S.dist) d = d + (d + 5 <= hi ? 5 : -5);
    S.dist = clamp(d, DMIN, DMAX);
    distIn.value = String(S.dist);
    bucketHot = false; bucketGlow = 0;
    setPill("", "bucket moved to " + S.dist + " m");
    changed("Bucket moved to " + S.dist + " metres.", true);
  });

  clearBtn.addEventListener("click", function () {
    trails.length = 0; S.sel = -1; renderShots(); fitHeight(); requestFrame();
    say("Paths cleared.");
  });

  shotsUl.addEventListener("click", function (e) {
    var b = e.target.closest ? e.target.closest("button[data-id]") : null;
    if (!b) return;
    var id = +b.getAttribute("data-id"), i, t = null;
    for (i = 0; i < trails.length; i++) if (trails[i].id === id) t = trails[i];
    if (!t) return;
    S.sel = id; S.angle = t.angle; S.power = t.power; S.ball = t.ball; S.air = t.air;
    angleIn.value = String(S.angle); powerIn.value = String(S.power);
    airBtn.setAttribute("aria-pressed", String(S.air));
    airBtn.lastChild.nodeValue = S.air ? "Air is on" : "Air is off";
    var kids = ballsBox.querySelectorAll("button");
    for (i = 0; i < kids.length; i++) kids[i].setAttribute("aria-pressed", String(i === S.ball));
    setPill("", "loaded shot #" + id);
    renderShots();
    changed("Loaded shot " + id + ": " + t.angle + " degrees, " + fx(t.power, 1) + " metres per second.", true);
  });

  /* drag-to-aim: pull the pouch back away from where you want the ball to go */
  var aiming = false, aimId = null, aimPx = 0, aimPy = 0, aimMoved = false, aimX0 = 0, aimY0 = 0;

  var grabAt = "";
  function positionGrab() {
    if (!scale) return;
    var key = Math.round(px(0)) + ":" + Math.round(py(H0));
    if (key === grabAt) return;
    grabAt = key;
    grab.style.left = Math.round(px(0)) + "px";
    grab.style.top = Math.round(py(H0)) + "px";
  }

  function aimFrom(clientX, clientY) {
    var r = cv.getBoundingClientRect();
    var lx = px(0), ly = py(H0);
    aimPx = clamp(clientX - r.left, 2, CW - 2);
    aimPy = clamp(clientY - r.top, 2, CH - 2);
    var dx = lx - (clientX - r.left), dy = (clientY - r.top) - ly;   /* pull back = aim forward */
    if (dx < 0.5) dx = 0.5;
    var ang = Math.atan2(Math.max(0, dy), dx) * 180 / Math.PI;
    if (dy <= 0) ang = 5;
    S.angle = Math.round(clamp(ang, 5, 85));
    var dist = Math.sqrt(dx * dx + dy * dy);
    var full = Math.max(60, Math.min(CW, CH) * 0.42);
    var f = clamp((dist - 12) / (full - 12), 0, 1);
    S.power = Math.round((8 + f * 26) * 2) / 2;
    angleIn.value = String(S.angle);
    powerIn.value = String(S.power);
    changed();
  }

  function startAim(e) {
    if (aiming || flight) return;
    aiming = true; aimId = e.pointerId; aimMoved = false;
    aimX0 = e.clientX; aimY0 = e.clientY;
    hideHint();
    setPill("busy", "pulling back…");
    try { e.currentTarget.setPointerCapture(e.pointerId); } catch (err) {}
    requestFrame();
    /* preventDefault below suppresses the compatibility mousedown, and with it the
       implicit focus — so hand the field its focus by hand or the arrow keys die */
    e.preventDefault();
    try { cv.focus({ preventScroll: true }); } catch (err) { cv.focus(); }
  }
  function moveAim(e) {
    if (!aiming || e.pointerId !== aimId) return;
    /* a tap without a drag is just "launch as aimed" — don't yank the aim to it */
    if (!aimMoved && Math.abs(e.clientX - aimX0) + Math.abs(e.clientY - aimY0) < 7) return;
    aimMoved = true;
    aimFrom(e.clientX, e.clientY);
    e.preventDefault();
  }
  function endAim(e) {
    if (!aiming || e.pointerId !== aimId) return;
    var onBall = e.currentTarget === grab;
    aiming = false; aimId = null;
    try { e.currentTarget.releasePointerCapture(e.pointerId); } catch (err) {}
    /* a click on open field just focuses it; the ball itself always launches */
    if (!aimMoved && !onBall) { setPill("", "ready — arrows aim, Enter launches"); requestFrame(); return; }
    launch();
    e.preventDefault();
  }
  function cancelAim(e) {
    if (!aiming) return;
    aiming = false; aimId = null;
    setPill("", "aim cancelled");
    requestFrame();
  }

  [grab, cv].forEach(function (el) {
    el.addEventListener("pointerdown", function (e) {
      /* touch only aims from the grab handle, so the page still scrolls */
      if (el === cv && e.pointerType === "touch") return;
      startAim(e);
    });
    el.addEventListener("pointermove", moveAim);
    el.addEventListener("pointerup", endAim);
    el.addEventListener("pointercancel", cancelAim);
    /* released outside the window: without this the aim latches on forever */
    el.addEventListener("lostpointercapture", cancelAim);
  });

  cv.addEventListener("keydown", function (e) {
    var k = e.key, step = e.shiftKey ? 5 : 1, handled = true;
    if (k === "ArrowLeft")      { S.angle = clamp(S.angle - step, 5, 85); angleIn.value = String(S.angle); }
    else if (k === "ArrowRight"){ S.angle = clamp(S.angle + step, 5, 85); angleIn.value = String(S.angle); }
    else if (k === "ArrowUp")   { S.power = clamp(S.power + step * 0.5, 8, 34); powerIn.value = String(S.power); }
    else if (k === "ArrowDown") { S.power = clamp(S.power - step * 0.5, 8, 34); powerIn.value = String(S.power); }
    else if (k === "Enter" || k === " " || k === "Spacebar") { launch(); }
    else handled = false;
    if (handled) {
      e.preventDefault();
      hideHint();
      if (k !== "Enter" && k !== " " && k !== "Spacebar") {
        changed(S.angle + " degrees, " + fx(S.power, 1) + " metres per second.");
        refitSoon();
      }
    }
  });
  cv.addEventListener("focus", hideHint);

  /* ── boot ───────────────────────────────────────────────────────────────── */
  readColors();
  renderBalls();
  renderShots();
  resize();
  recompute();
  computeScale();
  /* fit the box to the flight before the first paint, with no transition */
  field.style.transition = "none";
  fitHeight();
  void field.offsetHeight;
  field.style.transition = "";
  resize();
  computeScale();
  scale = scaleTarget;
  positionGrab();
  updateReadout();
  requestFrame();

  if (window.ResizeObserver) {
    var ro = new ResizeObserver(function () {
      var had = measured;
      resize(); computeScale(); positionGrab();
      /* width changed (or arrived at last, if we booted inside a hidden box) —
         the box has to be re-shaped to the flight, debounced so a drag is smooth */
      if (measured) { if (!had) { scale = scaleTarget; fitHeight(); } else refitSoon(); }
    });
    ro.observe(field);
  }
  if (!measured) {
    /* booted with no box at all (hidden tab, collapsed iframe). ResizeObserver
       usually catches the reveal, but it is not delivered in every embedding —
       poll for a short while so the field can never stay permanently blank. */
    var tries = 0, poll = setInterval(function () {
      resize();
      if (measured) { computeScale(); scale = scaleTarget; fitHeight(); positionGrab(); requestFrame(); }
      if (measured || ++tries > 100) clearInterval(poll);
    }, 120);
  }
  window.addEventListener("resize", function () { resize(); computeScale(); refitSoon(); });

  /* open already doing something: one shot lands just short of the bucket */
  setTimeout(function () { if (!flight && S.fired === 0) launch(true); }, reduced() ? 120 : 700);

})();
</script>
</body>
</html>