Falling Objects Race

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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">
<meta name="color-scheme" content="light dark">
<title>Falling Objects Race — sloprun.dev</title>
<link rel="icon" href="data:,">
<style>
/* ── sloprun design tokens (verbatim from demos/tokens.css) ───────────────── */
/* sloprun design tokens — inline this block into every demo (self-contained rule).
   Identity: instrument-panel. Machine facts in mono; human words in sans.
   Green is EARNED: only for "it ran / it worked" states, never decoration. */
: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); }

/* ── lane series colours (theme-matched, never green) ─────────────────────── */
:root { --s1: #B0472B; --s2: #1F6F8B; --s3: #6E4AA6; }
@media (prefers-color-scheme: dark) {
  :root:not([data-theme="light"]) { --s1: #FF9E6B; --s2: #5CC8E8; --s3: #C0A0F5; }
}
:root[data-theme="dark"] { --s1: #FF9E6B; --s2: #5CC8E8; --s3: #C0A0F5; }
:root[data-theme="dark"] { color-scheme: dark; }
:root[data-theme="light"] { color-scheme: light; }

/* ── base ─────────────────────────────────────────────────────────────────── */
*, *::before, *::after { box-sizing: border-box; }
html, body { margin: 0; padding: 0; }
body { line-height: 1.5; font-size: 15px; overflow-x: hidden; -webkit-text-size-adjust: 100%; }
.wrap { max-width: 1140px; margin: 0 auto; padding: 18px 14px 26px; }
h1, h2 { margin: 0; font-weight: 600; letter-spacing: -0.01em; }
.mono { font-family: var(--font-mono); font-variant-numeric: tabular-nums; }
:focus-visible { outline: 2px solid var(--accent); outline-offset: 2px; border-radius: 5px; }
.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;
}

/* ── header ───────────────────────────────────────────────────────────────── */
.head {
  display: flex; flex-wrap: wrap; gap: 10px 16px; align-items: flex-start;
  justify-content: space-between; padding-bottom: 13px; margin-bottom: 14px;
  border-bottom: 1px solid var(--line);
}
.head h1 { font-size: 1.3rem; }
.lede { margin: 5px 0 0; color: var(--muted); max-width: 66ch; font-size: 0.95rem; }
.status {
  display: inline-flex; align-items: center; gap: 8px; flex: none;
  font-family: var(--font-mono); font-size: 0.72rem; letter-spacing: 0.05em;
  padding: 6px 11px; border: 1px solid var(--line); border-radius: 999px;
  background: var(--surface); color: var(--muted); white-space: nowrap;
}
.status .dot { width: 8px; height: 8px; border-radius: 50%; background: var(--muted); flex: none; }
.status[data-state="run"] { color: var(--accent); border-color: var(--accent); background: var(--accent-soft); }
.status[data-state="run"] .dot { background: var(--accent); animation: pulse 1.15s ease-in-out infinite; }
@keyframes pulse { 0%,100% { opacity: 1 } 50% { opacity: 0.2 } }

/* ── layout ───────────────────────────────────────────────────────────────── */
.grid {
  display: grid; gap: 14px; align-items: stretch;
  grid-template-columns: minmax(0, 1fr) 330px;
  grid-template-areas: "tower readout" "tower lanes" "chart controls" "chart .";
  grid-template-rows: auto auto auto 1fr;
}
@media (max-width: 940px) {
  .grid { grid-template-columns: minmax(0, 1fr); grid-template-rows: none;
          grid-template-areas: "readout" "tower" "chart" "lanes" "controls"; }
}
/* the tower spans two rows next to two stacked panels — let it fill that
   height instead of leaving a hole under it */
.a-tower { grid-area: tower; display: flex; flex-direction: column }
.a-chart { grid-area: chart; display: flex; flex-direction: column }
.a-readout { grid-area: readout } .a-lanes { grid-area: lanes } .a-controls { grid-area: controls }
.a-readout, .a-lanes, .a-controls { align-self: start }
.panel {
  background: var(--surface); border: 1px solid var(--line);
  border-radius: var(--radius); padding: 13px; min-width: 0;
}
.panel > h2 {
  font-family: var(--font-mono); font-size: 0.68rem; text-transform: uppercase;
  letter-spacing: 0.1em; color: var(--muted); font-weight: 600; margin-bottom: 10px;
}
.panel > h2 .side { float: right; text-transform: none; letter-spacing: 0.04em; }

/* ── pickers over the lanes ───────────────────────────────────────────────── */
.picks { display: grid; grid-template-columns: repeat(3, minmax(0, 1fr)); gap: 7px; margin-bottom: 10px; }
.pick { min-width: 0; display: flex; flex-direction: column; gap: 4px; }
.pick .tag {
  font-family: var(--font-mono); font-size: 0.62rem; letter-spacing: 0.09em;
  text-transform: uppercase; color: var(--muted); display: flex; align-items: center; gap: 5px;
}
.pick .tag i { width: 8px; height: 8px; border-radius: 2px; flex: none; }
select {
  font: inherit; font-size: 0.8rem; width: 100%; min-width: 0;
  padding: 6px 7px; border-radius: 8px; border: 1px solid var(--line);
  background: var(--surface); color: var(--ink); cursor: pointer;
}
select:hover { border-color: var(--accent); }

/* ── canvases ─────────────────────────────────────────────────────────────── */
.tower { position: relative; width: 100%; flex: 1 1 auto;
         min-height: clamp(330px, 62vh, 540px); }
.chartbox { position: relative; width: 100%; flex: 1 1 auto;
            min-height: clamp(190px, 27vh, 260px); }
.tower canvas, .chartbox canvas {
  position: absolute; inset: 0; width: 100%; height: 100%; display: block;
  border-radius: 8px; border: 1px solid var(--line); background: var(--surface);
}
.caption {
  margin: 9px 0 0; font-family: var(--font-mono); font-size: 0.69rem;
  color: var(--muted); line-height: 1.6; letter-spacing: 0.01em;
}
.caption b { color: var(--ink); font-weight: 600; }

/* ── readout ──────────────────────────────────────────────────────────────── */
.clockrow { display: flex; align-items: flex-end; justify-content: space-between; gap: 10px; }
.big {
  font-family: var(--font-mono); font-variant-numeric: tabular-nums;
  font-size: clamp(2.3rem, 8.5vw, 3.1rem); font-weight: 600; line-height: 1.02;
  letter-spacing: -0.035em;
}
.big u { text-decoration: none; font-size: 0.4em; color: var(--muted); margin-left: 4px; }
.big small { display: block; font-size: 0.7rem; font-weight: 500; letter-spacing: 0.1em;
  text-transform: uppercase; color: var(--muted); margin-top: 7px; }
.warp {
  font-family: var(--font-mono); font-size: 0.72rem; color: var(--muted);
  border: 1px solid var(--line); border-radius: 999px; padding: 3px 9px; white-space: nowrap;
  background: var(--bg); flex: none; margin-bottom: 4px;
}
.warp[data-hot="1"] { color: var(--accent); border-color: var(--accent); background: var(--accent-soft); }
.fit {
  display: flex; align-items: flex-start; gap: 9px; margin-top: 12px; padding: 9px 10px;
  border: 1px solid var(--line); border-radius: 8px; background: var(--bg);
  font-size: 0.79rem; color: var(--muted); line-height: 1.4;
}
.fit .v { font-family: var(--font-mono); font-variant-numeric: tabular-nums;
  font-weight: 600; font-size: 0.86rem; color: var(--ink); flex: none; }
.fit[data-ok="1"] { border-color: var(--run); background: var(--run-soft); color: var(--run); }
.fit[data-ok="1"] .v { color: var(--run); }

/* ── lane cards ───────────────────────────────────────────────────────────── */
.lane { padding: 9px 0; border-top: 1px solid var(--line); }
.lane:first-child { border-top: 0; padding-top: 2px; }
.lrow { display: flex; align-items: baseline; gap: 8px; }
.lrow i { width: 9px; height: 9px; border-radius: 2px; flex: none; align-self: center; }
.lrow b { font-weight: 600; font-size: 0.87rem; flex: 1 1 auto; min-width: 0;
  overflow: hidden; text-overflow: ellipsis; white-space: nowrap; }
.lrow .now { font-family: var(--font-mono); font-variant-numeric: tabular-nums;
  font-size: 0.92rem; font-weight: 600; white-space: nowrap; }
.bar { height: 5px; border-radius: 3px; background: var(--line); margin: 6px 0 6px; overflow: hidden; }
.bar > i { display: block; height: 100%; width: 0; border-radius: 3px; transition: width 90ms linear; }
.meta { font-family: var(--font-mono); font-size: 0.68rem; color: var(--muted); line-height: 1.65;
  letter-spacing: 0.01em; word-break: break-word; }
.meta b { color: var(--ink); font-weight: 600; }
.meta .win { color: var(--accent); font-weight: 600; }

/* ── controls ─────────────────────────────────────────────────────────────── */
.ctl { display: grid; gap: 13px; }
.field label, .flab { display: flex; align-items: baseline; justify-content: space-between; gap: 10px;
  font-size: 0.8rem; color: var(--muted); margin-bottom: 5px; }
.field label .n, .flab .n { font-family: var(--font-mono); font-variant-numeric: tabular-nums;
  color: var(--ink); font-size: 0.85rem; font-weight: 600; }
input[type=range] {
  -webkit-appearance: none; appearance: none; width: 100%; height: 22px;
  background: none; margin: 0; display: block; cursor: pointer;
}
input[type=range]::-webkit-slider-runnable-track { height: 4px; border-radius: 2px; background: var(--line); }
input[type=range]::-moz-range-track { height: 4px; border-radius: 2px; background: var(--line); }
input[type=range]::-webkit-slider-thumb {
  -webkit-appearance: none; appearance: none; width: 16px; height: 16px; margin-top: -6px;
  border-radius: 50%; background: var(--accent); border: 2px solid var(--surface);
  box-shadow: 0 0 0 1px var(--accent);
}
input[type=range]::-moz-range-thumb {
  width: 14px; height: 14px; border-radius: 50%; background: var(--accent);
  border: 2px solid var(--surface); box-shadow: 0 0 0 1px var(--accent);
}
.btns, .seg { display: flex; flex-wrap: wrap; gap: 8px; }
.seg { gap: 6px; }
.btn {
  flex: 1 1 auto; min-width: 78px; font: inherit; font-size: 0.82rem;
  font-family: var(--font-mono); letter-spacing: 0.02em;
  padding: 8px 10px; border-radius: 8px; cursor: pointer;
  border: 1px solid var(--line); background: var(--surface); color: var(--ink);
}
.btn:hover:not(:disabled) { border-color: var(--accent); color: var(--accent); }
.btn.primary { border-color: var(--accent); background: var(--accent-soft); color: var(--accent); font-weight: 600; }
.btn[aria-pressed="true"] { border-color: var(--accent); background: var(--accent-soft); color: var(--accent); font-weight: 600; }
.btn:disabled { opacity: 0.42; cursor: not-allowed; }
.btn.sm { font-size: 0.72rem; padding: 6px 8px; min-width: 0; }
.check { display: flex; align-items: flex-start; gap: 9px; font-size: 0.79rem; color: var(--muted); cursor: pointer; }
.check input { margin: 2px 0 0; accent-color: var(--accent); width: 15px; height: 15px; flex: none; }
.check b { color: var(--ink); font-weight: 600; display: block; }
.keys { margin: 2px 0 0; font-family: var(--font-mono); font-size: 0.67rem; color: var(--muted); line-height: 1.7; }
.keys kbd { border: 1px solid var(--line); border-radius: 4px; padding: 0 4px; background: var(--bg); font: inherit; }

footer {
  margin-top: 18px; padding-top: 11px; border-top: 1px solid var(--line);
  font-family: var(--font-mono); font-size: 0.7rem; color: var(--muted); letter-spacing: 0.04em;
}

@media (prefers-reduced-motion: reduce) {
  * { animation-duration: 0.001ms !important; animation-iteration-count: 1 !important;
      transition-duration: 0.001ms !important; }
}
</style>
</head>
<body>
<div class="wrap">
  <header class="head">
    <div>
      <h1>Falling Objects Race</h1>
      <p class="lede">Three everyday things, dropped from the same height at the same moment. Air pushes back harder
        the faster you go — until it pushes exactly as hard as gravity pulls, and the speed stops rising. Take the air
        away and the race is a dead heat.</p>
    </div>
    <div class="status" id="status" data-state="run"><span class="dot"></span><span id="statusText">FALLING</span></div>
  </header>

  <main class="grid">
    <section class="panel a-tower">
      <div class="picks" id="picks">
        <div class="pick">
          <label class="tag" for="obj0"><i style="background:var(--s1)"></i> Lane 1</label>
          <select id="obj0"></select>
        </div>
        <div class="pick">
          <label class="tag" for="obj1"><i style="background:var(--s2)"></i> Lane 2</label>
          <select id="obj1"></select>
        </div>
        <div class="pick">
          <label class="tag" for="obj2"><i style="background:var(--s3)"></i> Lane 3</label>
          <select id="obj2"></select>
        </div>
      </div>
      <div class="tower">
        <canvas id="tower" role="img" aria-label="Three objects falling side by side" aria-describedby="desc"></canvas>
      </div>
      <p class="caption" id="towerCap"></p>
    </section>

    <section class="panel a-readout">
      <h2>Race clock</h2>
      <div class="clockrow">
        <div class="big"><span id="clock">0.00</span><u>s</u><small id="clockSub">since release</small></div>
        <span class="warp mono" id="warp">TIME ×1</span>
      </div>
      <div class="fit" id="fit" data-ok="0">
        <span class="v" id="fitv">—</span>
        <span id="fitmsg">Waiting for the first landing.</span>
      </div>
    </section>

    <section class="panel a-lanes">
      <h2>Readout <span class="side" id="modeTag">air</span></h2>
      <div id="lanes"></div>
      <p class="keys" id="laneNote">Drag is how bluff a shape is: a flat sheet is about 1.3, a smooth ball about 0.5.</p>
    </section>

    <section class="panel a-chart">
      <h2>Speed curves <span class="side" id="chartTag"></span></h2>
      <div class="chartbox">
        <canvas id="chart" role="img" aria-label="Speed curves for the three falling objects" aria-describedby="cdesc"></canvas>
      </div>
      <div class="seg" style="margin-top:10px" role="group" aria-label="Chart axes">
        <button class="btn sm" id="xDist" type="button" aria-pressed="true">x: distance</button>
        <button class="btn sm" id="xTime" type="button" aria-pressed="false">x: time</button>
        <button class="btn sm" id="yLin" type="button" aria-pressed="true">y: linear</button>
        <button class="btn sm" id="yLog" type="button" aria-pressed="false">y: log</button>
      </div>
      <p class="caption" id="chartCap"></p>
    </section>

    <section class="panel a-controls">
      <h2>Controls</h2>
      <div class="ctl">
        <div>
          <span class="flab"><span>Air around them</span><span class="n" id="airN">ON</span></span>
          <div class="seg" role="group" aria-label="Air or vacuum">
            <button class="btn" id="mAir" type="button" aria-pressed="true">Air</button>
            <button class="btn" id="mVac" type="button" aria-pressed="false">Vacuum</button>
          </div>
        </div>
        <div class="field">
          <label for="height">Drop height <span class="n" id="heightN">50 m</span></label>
          <input type="range" id="height" min="5" max="150" step="5" value="50">
          <p class="keys" id="storeys"></p>
        </div>
        <div class="btns">
          <button class="btn primary" id="drop" type="button">Drop again</button>
          <button class="btn" id="pause" type="button">Pause</button>
        </div>
        <div class="btns">
          <button class="btn" id="replay" type="button" disabled>Slow-mo the landings</button>
        </div>
        <label class="check" for="anim">
          <input type="checkbox" id="anim" checked>
          <span><b>Animate the fall</b>Off = every drop resolves instantly, no motion.</span>
        </label>
        <p class="keys"><kbd>D</kbd> drop · <kbd>V</kbd> air/vacuum · <kbd>R</kbd> slow-mo · <kbd>Space</kbd> pause</p>
      </div>
    </section>
  </main>

  <footer>demo · sloprun.dev</footer>
</div>

<div class="sr-only" id="desc"></div>
<div class="sr-only" id="cdesc"></div>
<div class="sr-only" role="status" aria-live="polite" id="live"></div>

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

  var root = document.documentElement;
  var $ = function (id) { return document.getElementById(id); };
  var live = $("live"), desc = $("desc"), cdesc = $("cdesc");
  var towerCv = $("tower"), chartCv = $("chart");

  /* ── constants ──────────────────────────────────────────────────────────── */
  var G = 9.80665;      /* metres per second squared */
  var RHO = 1.225;      /* air density at sea level, kg per cubic metre */
  var MONO = 'ui-monospace, SFMono-Regular, "SF Mono", Menlo, Consolas, monospace';
  var SANS = 'system-ui, -apple-system, "Segoe UI", sans-serif';

  /* mass kg · frontal area m^2 · drag coefficient · draw size · shape */
  var OBJECTS = [
    { id: "feather",  name: "Feather",      m: 0.0008, a: 0.0110, cd: 1.40, r: 15, s: "feather" },
    { id: "paper",    name: "Paper sheet",  m: 0.0045, a: 0.0623, cd: 1.30, r: 19, s: "sheet" },
    { id: "umbrella", name: "Open umbrella",m: 0.4500, a: 0.6000, cd: 1.40, r: 25, s: "umbrella" },
    { id: "beach",    name: "Beach ball",   m: 0.1500, a: 0.1134, cd: 0.47, r: 22, s: "beach" },
    { id: "pingpong", name: "Ping-pong",    m: 0.0027, a: 0.00126,cd: 0.47, r: 7,  s: "plain" },
    { id: "coin",     name: "Coin",         m: 0.0057, a: 0.00045,cd: 1.20, r: 8,  s: "coin" },
    { id: "tennis",   name: "Tennis ball",  m: 0.0580, a: 0.00358,cd: 0.50, r: 11, s: "tennis" },
    { id: "basket",   name: "Basketball",   m: 0.6200, a: 0.04558,cd: 0.47, r: 19, s: "basket" },
    { id: "brick",    name: "Brick",        m: 2.3000, a: 0.0171, cd: 1.10, r: 19, s: "brick" },
    { id: "bowling",  name: "Bowling ball", m: 6.3500, a: 0.03664,cd: 0.50, r: 16, s: "bowling" }
  ];
  var byId = {};
  for (var oi = 0; oi < OBJECTS.length; oi++) byId[OBJECTS[oi].id] = OBJECTS[oi];

  /* ── physics (closed form — quadratic drag from rest) ────────────────────── */
  function termV(o) { return Math.sqrt((2 * o.m * G) / (RHO * o.cd * o.a)); }
  function lncosh(x) { return x > 20 ? x - Math.LN2 : Math.log(Math.cosh(x)); }
  function fallenAir(vt, t) { return (vt * vt / G) * lncosh(G * t / vt); }
  function speedAir(vt, t) { return vt * Math.tanh(G * t / vt); }
  function speedAirAtY(vt, y) { return vt * Math.sqrt(Math.max(0, 1 - Math.exp(-2 * G * y / (vt * vt)))); }
  function landTimeAir(vt, h) {
    var x = G * h / (vt * vt), a;
    if (x > 20) { a = x + Math.LN2; }
    else { var e = Math.exp(x); a = Math.log(e + Math.sqrt(Math.max(0, e * e - 1))); }
    return vt / G * a;
  }
  function landTimeVac(h) { return Math.sqrt(2 * h / G); }

  /* ── state ──────────────────────────────────────────────────────────────── */
  var S = {
    ids: ["feather", "tennis", "brick"],
    lanes: [],
    H: 50,
    air: true,
    t: 0,
    state: "falling",     /* falling | paused | done | replay */
    paused: "falling",    /* what to resume into */
    rate: 1, rateTarget: 1,
    view: { b0: 0, b1: 50, t0: 0, t1: 50 },
    chartX: "dist", chartY: "lin",
    segs: [], segIdx: -1,
    announced: [],
    animate: true
  };
  var REPLAY_RATE = 0.30;

  var mqRM = window.matchMedia ? matchMedia("(prefers-reduced-motion: reduce)") : null;
  var reduced = !!(mqRM && mqRM.matches);
  if (reduced) { S.animate = false; $("anim").checked = false; }
  if (mqRM) {
    var onRM = function () {
      reduced = mqRM.matches;
      if (reduced && S.animate) { S.animate = false; $("anim").checked = false; restart(true); }
    };
    if (mqRM.addEventListener) mqRM.addEventListener("change", onRM);
    else if (mqRM.addListener) mqRM.addListener(onRM);
  }

  /* ── theme ──────────────────────────────────────────────────────────────── */
  var C = {};
  function hx(h) {
    h = String(h).trim();
    if (h.charAt(0) === "#") {
      if (h.length === 4) return [parseInt(h[1] + h[1], 16), parseInt(h[2] + h[2], 16), parseInt(h[3] + h[3], 16)];
      return [parseInt(h.substr(1, 2), 16), parseInt(h.substr(3, 2), 16), parseInt(h.substr(5, 2), 16)];
    }
    return [128, 128, 128];
  }
  function rgba(c, a) { return "rgba(" + c[0] + "," + c[1] + "," + c[2] + "," + a + ")"; }
  function rgb(c) { return "rgb(" + c[0] + "," + c[1] + "," + c[2] + ")"; }
  function readTheme() {
    var s = getComputedStyle(root);
    C.surface = hx(s.getPropertyValue("--surface"));
    C.bg = hx(s.getPropertyValue("--bg"));
    C.ink = hx(s.getPropertyValue("--ink"));
    C.muted = hx(s.getPropertyValue("--muted"));
    C.line = hx(s.getPropertyValue("--line"));
    C.accent = hx(s.getPropertyValue("--accent"));
    C.run = hx(s.getPropertyValue("--run"));
    C.s = [hx(s.getPropertyValue("--s1")), hx(s.getPropertyValue("--s2")), hx(s.getPropertyValue("--s3"))];
  }
  readTheme();
  window.addEventListener("message", function (e) {
    var d = e.data;
    if (d && d.type === "sloprun:theme" && (d.theme === "light" || d.theme === "dark")) {
      root.setAttribute("data-theme", d.theme); readTheme(); draw();
    }
  });
  var mqDark = window.matchMedia ? matchMedia("(prefers-color-scheme: dark)") : null;
  if (mqDark) {
    var onScheme = function () { readTheme(); draw(); };
    if (mqDark.addEventListener) mqDark.addEventListener("change", onScheme);
    else if (mqDark.addListener) mqDark.addListener(onScheme);
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  /* the canvases bake the palette in, so re-read it however the theme arrives —
     postMessage, media query, or the attribute being set on <html> directly */
  if (window.MutationObserver) {
    new MutationObserver(function () { readTheme(); draw(); })
      .observe(root, { attributes: true, attributeFilter: ["data-theme", "style", "class"] });
  }

  /* ── format helpers ─────────────────────────────────────────────────────── */
  function clamp(v, a, b) { return v < a ? a : v > b ? b : v; }
  function f2(v) { return v.toFixed(2); }
  function sp(v) { return (v >= 100 ? v.toFixed(0) : v.toFixed(v < 10 ? 2 : 1)); }
  function secs(v) { return v >= 100 ? v.toFixed(1) : v.toFixed(2); }
  function kmh(v) { return (v * 3.6).toFixed(v * 3.6 >= 100 ? 0 : 1); }
  function gram(m) { return m < 1 ? (m * 1000).toFixed(m < 0.01 ? 1 : 0) + " g" : m.toFixed(2) + " kg"; }
  function areaCm(a) { return a >= 0.1 ? (a * 10000).toFixed(0) + " cm2" : (a * 10000).toFixed(a < 0.005 ? 1 : 0) + " cm2"; }
  function rateTxt(r) { return r < 1 ? "×" + r.toFixed(2) : r < 10 ? "×" + r.toFixed(1) : "×" + Math.round(r); }
  /* axis tick label: zero always prints bare, so a 0/10/20 axis never reads "0.0" */
  function tick(v, step) { return v === 0 ? "0" : step < 1 ? v.toFixed(1) : String(Math.round(v)); }
  function niceStep(x) {
    if (!(x > 0)) return 1;
    var p = Math.pow(10, Math.floor(Math.log(x) / Math.LN10)), f = x / p;
    return (f < 1.5 ? 1 : f < 3 ? 2 : f < 7 ? 5 : 10) * p;
  }

  /* ── lane model ─────────────────────────────────────────────────────────── */
  function rebuild() {
    S.lanes = [];
    for (var i = 0; i < 3; i++) {
      var o = byId[S.ids[i]];
      var vt = termV(o);
      var tl = S.air ? landTimeAir(vt, S.H) : landTimeVac(S.H);
      var vi = S.air ? speedAir(vt, tl) : G * tl;
      S.lanes.push({ o: o, i: i, vt: vt, tLand: tl, vImp: vi });
    }
  }
  function fallenAt(L, t) {
    var tt = Math.min(t, L.tLand);
    return S.air ? Math.min(S.H, fallenAir(L.vt, tt)) : Math.min(S.H, 0.5 * G * tt * tt);
  }
  function speedAt(L, t) {
    var tt = Math.min(t, L.tLand);
    return S.air ? speedAir(L.vt, tt) : G * tt;
  }
  /* true when all three trace one and the same speed curve: always in vacuum,
     and in air whenever the three objects have matching terminal speeds */
  function coincident() {
    if (!S.air) return true;
    var lo = Infinity, hi = 0;
    for (var i = 0; i < 3; i++) { var v = S.lanes[i].vt; if (v < lo) lo = v; if (v > hi) hi = v; }
    return hi - lo < hi * 0.002;
  }
  function tMax() { var m = 0; for (var i = 0; i < 3; i++) m = Math.max(m, S.lanes[i].tLand); return m; }
  function tMin() { var m = Infinity; for (var i = 0; i < 3; i++) m = Math.min(m, S.lanes[i].tLand); return m; }
  function nextLanding(t) {
    var n = null;
    for (var i = 0; i < 3; i++) { var x = S.lanes[i].tLand; if (x > t + 1e-6 && (n === null || x < n)) n = x; }
    return n;
  }
  function setRateTarget(first) {
    var n = nextLanding(S.t);
    if (n === null) { S.rateTarget = 1; return; }
    S.rateTarget = clamp((n - S.t) / (first ? 3.0 : 2.2), 0.2, 60);
  }

  /* ── run control ────────────────────────────────────────────────────────── */
  /* silent = true while a slider is being dragged, so the live region is not
     flooded with one announcement per pixel of travel */
  function restart(silent) {
    rebuild();
    S.t = 0; S.announced = [false, false, false]; S.segs = []; S.segIdx = -1;
    S.view.t0 = 0; S.view.t1 = S.H; S.view.b0 = 0; S.view.b1 = S.H;
    if (!S.animate) { S.t = tMax(); S.state = "done"; }
    else { S.state = "falling"; setRateTarget(true); S.rate = S.rateTarget; }
    syncButtons(); sync(); draw(); kick();
    if (!silent) {
      announce(S.air
        ? "Dropped from " + S.H + " metres through air."
        : "Dropped from " + S.H + " metres in a vacuum.");
    }
  }
  function startReplay() {
    if (!S.animate) return;
    S.segs = buildSegments();
    if (!S.segs.length) return;
    S.segIdx = 0; S.state = "replay"; S.t = S.segs[0].from;
    S.view.b0 = 0; S.view.b1 = S.segs[0].zoom;
    syncButtons(); sync(); draw(); kick();
    announce("Slow-motion replay of the landings.");
  }
  function buildSegments() {
    var order = [];
    for (var i = 0; i < 3; i++) order.push({ i: i, t: S.lanes[i].tLand });
    order.sort(function (a, b) { return a.t - b.t; });
    var groups = [];
    for (var k = 0; k < order.length; k++) {
      var last = groups[groups.length - 1];
      if (last && Math.abs(order[k].t - last.t) < 0.03) { last.ids.push(order[k].i); }
      else groups.push({ t: order[k].t, ids: [order[k].i] });
    }
    return groups.map(function (g) {
      var vmax = 0;
      for (var j = 0; j < g.ids.length; j++) vmax = Math.max(vmax, S.lanes[g.ids[j]].vImp);
      var zoom = clamp(vmax * 0.75, 1.2, S.H);
      var win = clamp(zoom / Math.max(vmax, 0.01), 0.30, 0.70);
      return { from: Math.max(0, g.t - win), to: g.t + Math.min(0.35, win * 0.6), zoom: zoom, ids: g.ids, at: g.t };
    });
  }

  /* ── animation loop ─────────────────────────────────────────────────────── */
  var raf = 0, last = 0;
  function kick() { if (!raf) { last = 0; raf = requestAnimationFrame(frame); } }
  function frame(ts) {
    raf = 0;
    var dt = last ? Math.min(0.05, (ts - last) / 1000) : 0.016;
    last = ts;

    if (S.state === "falling") {
      var k = 1 - Math.exp(-dt * 3.5);
      S.rate += (S.rateTarget - S.rate) * k;
      var prev = S.t;
      S.t += dt * S.rate;
      for (var i = 0; i < 3; i++) {
        var L = S.lanes[i];
        if (!S.announced[i] && S.t >= L.tLand) {
          S.announced[i] = true;
          announce(L.o.name + " landed at " + secs(L.tLand) + " seconds, hitting " + sp(L.vImp) + " metres per second.");
          setRateTarget(false);
        }
      }
      if (S.t >= tMax()) { S.t = tMax(); S.state = "done"; syncButtons(); }
    } else if (S.state === "replay") {
      S.t += dt * REPLAY_RATE;
      var seg = S.segs[S.segIdx];
      if (seg && S.t >= seg.to) {
        S.segIdx++;
        if (S.segIdx >= S.segs.length) { S.state = "done"; S.t = tMax(); S.view.b1 = S.H; syncButtons(); }
        else { S.t = S.segs[S.segIdx].from; S.view.b1 = S.segs[S.segIdx].zoom; }
      }
    }

    /* camera easing */
    var ck = 1 - Math.exp(-dt * 6);
    S.view.t0 += (S.view.b0 - S.view.t0) * ck;
    S.view.t1 += (S.view.b1 - S.view.t1) * ck;
    if (Math.abs(S.view.t1 - S.view.b1) < S.H * 0.002) S.view.t1 = S.view.b1;

    sync(); draw();
    if (S.state === "falling" || S.state === "replay" || Math.abs(S.view.t1 - S.view.b1) > 1e-4) kick();
  }

  function announce(msg) { live.textContent = msg; }

  /* ── canvas plumbing ────────────────────────────────────────────────────── */
  function fit(cv) {
    var r = cv.getBoundingClientRect();
    var dpr = Math.min(window.devicePixelRatio || 1, 2);
    var w = Math.max(1, Math.round(r.width)), h = Math.max(1, Math.round(r.height));
    if (cv.width !== Math.round(w * dpr) || cv.height !== Math.round(h * dpr)) {
      cv.width = Math.round(w * dpr); cv.height = Math.round(h * dpr);
    }
    var ctx = cv.getContext("2d");
    ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
    return { ctx: ctx, w: w, h: h };
  }

  /* ── object glyphs ──────────────────────────────────────────────────────── */
  function glyph(ctx, o, x, y, col, sc, stretch, spin) {
    var r = o.r * sc;
    ctx.save();
    ctx.translate(x, y);
    if (spin) ctx.rotate(spin);
    if (stretch && stretch > 1) ctx.scale(1 / Math.sqrt(stretch), stretch);
    ctx.lineWidth = Math.max(1, r * 0.09);
    ctx.strokeStyle = rgb(col);
    ctx.fillStyle = rgba(col, 0.30);
    var s = o.s;
    if (s === "feather") {
      ctx.beginPath();
      ctx.moveTo(0, -r);
      ctx.bezierCurveTo(r * 0.75, -r * 0.3, r * 0.55, r * 0.6, 0, r);
      ctx.bezierCurveTo(-r * 0.55, r * 0.6, -r * 0.75, -r * 0.3, 0, -r);
      ctx.fill(); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(0, -r * 0.95); ctx.lineTo(0, r * 1.05); ctx.stroke();
    } else if (s === "sheet") {
      ctx.beginPath();
      ctx.moveTo(-r, -r * 0.42); ctx.lineTo(r * 0.86, -r * 0.72);
      ctx.lineTo(r, r * 0.42); ctx.lineTo(-r * 0.86, r * 0.72);
      ctx.closePath(); ctx.fill(); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(-r * 0.5, -r * 0.55); ctx.lineTo(-r * 0.36, r * 0.66); ctx.stroke();
    } else if (s === "umbrella") {
      ctx.beginPath(); ctx.arc(0, r * 0.32, r, Math.PI, 0); ctx.closePath(); ctx.fill(); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(-r * 0.5, r * 0.32); ctx.lineTo(-r * 0.28, -r * 0.5); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(r * 0.5, r * 0.32); ctx.lineTo(r * 0.28, -r * 0.5); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(0, r * 0.32); ctx.lineTo(0, r * 1.3); ctx.stroke();
    } else if (s === "brick") {
      var bw = r * 1.25, bh = r * 0.62;
      ctx.beginPath();
      if (ctx.roundRect) ctx.roundRect(-bw, -bh, bw * 2, bh * 2, r * 0.14);
      else ctx.rect(-bw, -bh, bw * 2, bh * 2);
      ctx.fill(); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(-bw, 0); ctx.lineTo(bw, 0); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(-bw * 0.3, -bh); ctx.lineTo(-bw * 0.3, 0); ctx.stroke();
      ctx.beginPath(); ctx.moveTo(bw * 0.35, 0); ctx.lineTo(bw * 0.35, bh); ctx.stroke();
    } else if (s === "coin") {
      ctx.beginPath(); ctx.ellipse(0, 0, r, r * 0.34, 0, 0, Math.PI * 2); ctx.fill(); ctx.stroke();
      ctx.beginPath(); ctx.ellipse(0, 0, r * 0.55, r * 0.18, 0, 0, Math.PI * 2); ctx.stroke();
    } else {
      ctx.beginPath(); ctx.arc(0, 0, r, 0, Math.PI * 2); ctx.fill(); ctx.stroke();
      if (s === "tennis") {
        ctx.beginPath(); ctx.arc(-r * 1.15, 0, r * 1.35, -0.72, 0.72); ctx.stroke();
        ctx.beginPath(); ctx.arc(r * 1.15, 0, r * 1.35, Math.PI - 0.72, Math.PI + 0.72); ctx.stroke();
      } else if (s === "basket") {
        ctx.beginPath(); ctx.moveTo(-r, 0); ctx.lineTo(r, 0); ctx.stroke();
        ctx.beginPath(); ctx.moveTo(0, -r); ctx.lineTo(0, r); ctx.stroke();
        ctx.beginPath(); ctx.arc(-r * 1.3, 0, r * 1.1, -0.9, 0.9); ctx.stroke();
        ctx.beginPath(); ctx.arc(r * 1.3, 0, r * 1.1, Math.PI - 0.9, Math.PI + 0.9); ctx.stroke();
      } else if (s === "beach") {
        for (var q = 0; q < 3; q++) {
          ctx.beginPath();
          ctx.ellipse(0, 0, r * (0.28 + q * 0.3), r, 0, -Math.PI / 2, Math.PI / 2);
          ctx.stroke();
        }
      } else if (s === "bowling") {
        ctx.fillStyle = rgb(col);
        for (var d = 0; d < 3; d++) {
          ctx.beginPath();
          ctx.arc(Math.cos(d * 2.1 - 1.6) * r * 0.42, Math.sin(d * 2.1 - 1.6) * r * 0.42 - r * 0.05, r * 0.15, 0, Math.PI * 2);
          ctx.fill();
        }
      }
    }
    ctx.restore();
  }

  /* ── tower ──────────────────────────────────────────────────────────────── */
  var numbersShown = true;   /* set by drawTower: are per-object speed labels drawn? */
  function drawTower() {
    var f = fit(towerCv), ctx = f.ctx, w = f.w, h = f.h;
    ctx.clearRect(0, 0, w, h);
    ctx.fillStyle = rgb(C.surface); ctx.fillRect(0, 0, w, h);
    var gr = ctx.createLinearGradient(0, 0, 0, h);
    gr.addColorStop(0, rgba(C.line, 0.55)); gr.addColorStop(0.75, rgba(C.line, 0.05));
    ctx.fillStyle = gr; ctx.fillRect(0, 0, w, h);

    var padL = w < 380 ? 32 : 42, padR = 8, padT = 18, padB = 30;
    var groundY = h - padB, topY = padT, plotH = groundY - topY;
    var laneW = (w - padL - padR) / 3;
    var b0 = S.view.t0, b1 = Math.max(S.view.t1, 0.2);
    var span = b1 - b0;
    function ypx(above) { return groundY - (above - b0) / span * plotH; }
    var sc = clamp(laneW / 168, 0.5, 1.35) * clamp(Math.pow(S.H / span, 0.35), 1, 2.4);
    var zoomed = span < S.H * 0.98;

    /* ruler */
    var step = niceStep(span / 5);
    ctx.font = "10px " + MONO;
    ctx.textAlign = "right"; ctx.textBaseline = "middle";
    for (var m = Math.ceil(b0 / step) * step; m <= b1 + 1e-9; m += step) {
      var y = ypx(m);
      ctx.strokeStyle = rgba(C.line, 0.9); ctx.lineWidth = 1;
      ctx.beginPath(); ctx.moveTo(padL - 5, y + 0.5); ctx.lineTo(w - padR, y + 0.5); ctx.stroke();
      ctx.fillStyle = rgba(C.muted, 0.95);
      ctx.fillText(tick(m, step), padL - 9, y);
    }
    ctx.textAlign = "left";
    ctx.fillStyle = rgba(C.muted, 0.9);
    ctx.fillText("m", 4, topY - 6 < 8 ? 10 : topY - 6);

    /* release line */
    if (!zoomed) {
      var ry = ypx(S.H);
      ctx.strokeStyle = rgba(C.accent, 0.8); ctx.lineWidth = 1.5;
      ctx.setLineDash([5, 4]);
      ctx.beginPath(); ctx.moveTo(padL - 6, ry); ctx.lineTo(w - padR, ry); ctx.stroke();
      ctx.setLineDash([]);
    }

    /* lanes */
    for (var i = 0; i < 3; i++) {
      var cx = padL + laneW * (i + 0.5);
      ctx.strokeStyle = rgba(C.line, 0.85); ctx.lineWidth = 1;
      ctx.setLineDash([2, 5]);
      ctx.beginPath(); ctx.moveTo(cx, topY); ctx.lineTo(cx, groundY); ctx.stroke();
      ctx.setLineDash([]);
    }

    /* ground */
    ctx.fillStyle = rgba(C.line, 0.55);
    ctx.fillRect(0, groundY, w, h - groundY);
    ctx.strokeStyle = rgba(C.ink, 0.55); ctx.lineWidth = 2;
    ctx.beginPath(); ctx.moveTo(0, groundY + 1); ctx.lineTo(w, groundY + 1); ctx.stroke();
    ctx.strokeStyle = rgba(C.muted, 0.35); ctx.lineWidth = 1;
    for (var gx = -20; gx < w; gx += 9) {
      ctx.beginPath(); ctx.moveTo(gx, h); ctx.lineTo(gx + 14, groundY + 2); ctx.stroke();
    }

    var trailDt = Math.max(0.012, (S.state === "replay" ? REPLAY_RATE : S.rate) * 0.045);
    var showNum = laneW > 92;
    numbersShown = showNum;   /* the caption must not promise labels we dropped */

    for (var j = 0; j < 3; j++) {
      var L = S.lanes[j], col = C.s[j];
      var fallen = fallenAt(L, S.t);
      var above = S.H - fallen;
      var landed = S.t >= L.tLand - 1e-9;
      var v = speedAt(L, S.t);
      var cx2 = padL + laneW * (j + 0.5);
      var y2 = ypx(above);

      /* trail */
      if (S.animate && !landed) {
        for (var k = 1; k <= 7; k++) {
          var tk = S.t - k * trailDt;
          if (tk <= 0) break;
          var yk = ypx(S.H - fallenAt(L, tk));
          if (yk < topY - 40) break;
          ctx.fillStyle = rgba(col, 0.20 * (1 - k / 8));
          ctx.beginPath();
          ctx.ellipse(cx2, yk, L.o.r * sc * 0.42, L.o.r * sc * 0.30, 0, 0, Math.PI * 2);
          ctx.fill();
        }
      }

      /* off-view marker */
      if (y2 < topY - 4) {
        ctx.fillStyle = rgba(col, 0.85);
        ctx.beginPath();
        ctx.moveTo(cx2, topY - 1); ctx.lineTo(cx2 - 6, topY + 9); ctx.lineTo(cx2 + 6, topY + 9);
        ctx.closePath(); ctx.fill();
        if (showNum) {
          ctx.font = "10px " + MONO; ctx.textAlign = "center"; ctx.textBaseline = "top";
          ctx.fillStyle = rgba(C.muted, 0.95);
          ctx.fillText("still falling", cx2, topY + 12);
        }
        continue;
      }

      if (landed) {
        /* resting on the ground + impact tick */
        ctx.strokeStyle = rgba(col, 0.9); ctx.lineWidth = 2.5;
        ctx.beginPath(); ctx.moveTo(cx2 - laneW * 0.24, groundY); ctx.lineTo(cx2 + laneW * 0.24, groundY); ctx.stroke();
        glyph(ctx, L.o, cx2, groundY - L.o.r * sc * 0.55, col, sc, 1, 0);
        if (showNum) {
          ctx.font = "600 11px " + MONO; ctx.textAlign = "center"; ctx.textBaseline = "top";
          ctx.fillStyle = rgba(col, 1);
          ctx.fillText(sp(L.vImp) + " m/s", cx2, groundY + 8);
        }
      } else {
        var stretch = S.animate ? clamp(1 + v / Math.max(L.vt, 8) * 0.22, 1, 1.28) : 1;
        var spin = 0;
        if (S.animate && (L.o.s === "feather" || L.o.s === "sheet" || L.o.s === "coin")) {
          spin = Math.sin(S.t * (L.o.s === "coin" ? 9 : 2.4)) * 0.5;
        }
        glyph(ctx, L.o, cx2, y2, col, sc, stretch, spin);
        if (showNum) {
          ctx.font = "600 11px " + MONO; ctx.textAlign = "left"; ctx.textBaseline = "middle";
          ctx.fillStyle = rgba(col, 0.95);
          var lbl = sp(v);
          var lx = cx2 + L.o.r * sc + 7;
          if (lx + 34 > w - padR) { ctx.textAlign = "right"; lx = cx2 - L.o.r * sc - 7; }
          ctx.fillText(lbl, lx, y2);
        }
      }
    }

    /* slow-mo caption */
    if (S.state === "replay" && S.segs[S.segIdx]) {
      var seg = S.segs[S.segIdx];
      var names = seg.ids.map(function (id) { return S.lanes[id].o.name.toUpperCase(); }).join(" + ");
      var txt = "SLOW-MO " + rateTxt(REPLAY_RATE) + "  ·  " + names + "  ·  " + sp(S.lanes[seg.ids[0]].vImp) + " m/s";
      ctx.font = "600 11px " + MONO; ctx.textAlign = "center"; ctx.textBaseline = "middle";
      var tw = ctx.measureText(txt).width + 20;
      var bx = Math.max(4, w / 2 - tw / 2), by = topY + 2;
      ctx.fillStyle = rgba(C.bg, 0.94);
      ctx.strokeStyle = rgba(C.accent, 0.75); ctx.lineWidth = 1;
      ctx.beginPath();
      if (ctx.roundRect) ctx.roundRect(bx, by, Math.min(tw, w - 8), 22, 11);
      else ctx.rect(bx, by, Math.min(tw, w - 8), 22);
      ctx.fill(); ctx.stroke();
      ctx.fillStyle = rgb(C.accent);
      ctx.fillText(txt, bx + Math.min(tw, w - 8) / 2, by + 11);
    }
  }

  /* ── chart ──────────────────────────────────────────────────────────────── */
  function drawChart() {
    var f = fit(chartCv), ctx = f.ctx, w = f.w, h = f.h;
    ctx.clearRect(0, 0, w, h);
    ctx.fillStyle = rgb(C.surface); ctx.fillRect(0, 0, w, h);

    var padL = w < 380 ? 34 : 44, padR = w < 380 ? 10 : 16, padT = 12, padB = 31;
    var pw = w - padL - padR, ph = h - padT - padB;
    if (pw < 20 || ph < 20) return;

    var byDist = S.chartX === "dist";
    var xmax = byDist ? S.H : Math.max(tMax(), 0.1);
    var vmaxAll = 0, vminAll = Infinity;
    for (var i = 0; i < 3; i++) {
      vmaxAll = Math.max(vmaxAll, S.air ? S.lanes[i].vt : S.lanes[i].vImp);
      vminAll = Math.min(vminAll, S.lanes[i].vImp);
    }
    var logY = S.chartY === "log";
    var ymax = vmaxAll * 1.06;
    var ymin = logY ? Math.max(0.05, Math.min(vminAll * 0.45, ymax / 200)) : 0;

    function X(u) { return padL + (u / xmax) * pw; }
    function Y(v) {
      if (!logY) return padT + ph - clamp(v / ymax, 0, 1) * ph;
      var lv = Math.log(Math.max(v, ymin * 0.999)), a = Math.log(ymin), b = Math.log(ymax);
      return padT + ph - clamp((lv - a) / (b - a), 0, 1) * ph;
    }

    /* grid + axes */
    ctx.font = "10px " + MONO; ctx.fillStyle = rgba(C.muted, 0.95);
    ctx.strokeStyle = rgba(C.line, 0.9); ctx.lineWidth = 1;
    ctx.textAlign = "right"; ctx.textBaseline = "middle";
    var yticks = [];
    if (logY) {
      var dec = [1, 2, 5];
      for (var e = -2; e <= 3; e++) for (var d = 0; d < 3; d++) {
        var val = dec[d] * Math.pow(10, e);
        if (val >= ymin && val <= ymax) yticks.push(val);
      }
    } else {
      var ys0 = niceStep(ymax / 4);
      for (var yv = 0; yv <= ymax + 1e-9; yv += ys0) yticks.push(yv);
    }
    var ystep = logY ? 0.1 : niceStep(ymax / 4);
    for (var yi = 0; yi < yticks.length; yi++) {
      var yy = Math.round(Y(yticks[yi])) + 0.5;
      ctx.beginPath(); ctx.moveTo(padL, yy); ctx.lineTo(padL + pw, yy); ctx.stroke();
      ctx.fillText(tick(yticks[yi], logY ? (yticks[yi] < 1 ? 0.1 : 1) : ystep), padL - 6, yy);
    }
    ctx.textAlign = "center"; ctx.textBaseline = "top";
    var xs = niceStep(xmax / 4);
    for (var xv = 0; xv <= xmax + 1e-9; xv += xs) {
      var xx = Math.round(X(xv)) + 0.5;
      ctx.strokeStyle = rgba(C.line, 0.6);
      ctx.beginPath(); ctx.moveTo(xx, padT); ctx.lineTo(xx, padT + ph); ctx.stroke();
      ctx.fillStyle = rgba(C.muted, 0.95);
      ctx.fillText(tick(xv, xs), xx, padT + ph + 5);
    }
    ctx.textAlign = "left";
    ctx.fillStyle = rgba(C.muted, 0.9);
    ctx.fillText(byDist ? "metres fallen" : "seconds", padL + 2, padT + ph + 18);
    ctx.save();
    ctx.translate(11, padT + ph / 2); ctx.rotate(-Math.PI / 2);
    ctx.textAlign = "center"; ctx.textBaseline = "top";
    ctx.fillText("speed m/s", 0, 0);
    ctx.restore();

    /* terminal-speed asymptotes */
    if (S.air) {
      ctx.setLineDash([5, 4]); ctx.lineWidth = 1.25;
      for (var a = 0; a < 3; a++) {
        var ya = Y(S.lanes[a].vt);
        if (ya < padT - 2 || ya > padT + ph + 2) continue;
        ctx.strokeStyle = rgba(C.s[a], 0.55);
        ctx.beginPath(); ctx.moveTo(padL, ya); ctx.lineTo(padL + pw, ya); ctx.stroke();
      }
      ctx.setLineDash([]);
    }

    /* curves — "same" means all three trace one identical curve, so draw them
       nested (thick → thin, dashed) instead of hiding two under the third */
    var same = coincident();
    var widths = same ? [4.2, 2.4, 1.2] : [2.2, 2.2, 2.2];
    var dashes = same ? [[], [7, 5], [2, 4]] : [[], [], []];
    var placed = [];   /* label anchors already used, so two heads never collide */
    for (var c = 0; c < 3; c++) {
      var L = S.lanes[c];
      var prog = byDist ? fallenAt(L, S.t) : Math.min(S.t, L.tLand);
      var lim = byDist ? S.H : L.tLand;
      var upto = Math.min(prog, lim);
      if (upto <= 0) continue;
      var N = 140, px = 0, py = 0;
      ctx.strokeStyle = rgb(C.s[c]);
      ctx.lineWidth = widths[c]; ctx.setLineDash(dashes[c]);
      ctx.lineJoin = "round"; ctx.lineCap = "round";
      ctx.beginPath();
      for (var n = 0; n <= N; n++) {
        var u = upto * n / N, v;
        if (byDist) v = S.air ? speedAirAtY(L.vt, u) : Math.sqrt(2 * G * u);
        else v = S.air ? speedAir(L.vt, u) : G * u;
        px = X(u); py = Y(v);
        if (n === 0) ctx.moveTo(px, py); else ctx.lineTo(px, py);
      }
      ctx.stroke(); ctx.setLineDash([]);
      /* head / landing dot */
      var done = upto >= lim - 1e-9;
      ctx.fillStyle = rgb(C.s[c]);
      ctx.beginPath(); ctx.arc(px, py, done ? 3.6 : 3, 0, Math.PI * 2); ctx.fill();
      if (done && !same) {
        ctx.font = "600 10px " + MONO; ctx.textBaseline = "middle";
        var label = L.o.name;
        var lw = ctx.measureText(label).width;
        var ly = py - 8;
        for (var q = 0; q < placed.length; q++) {
          if (Math.abs(placed[q].x - px) < lw + 16 && Math.abs(placed[q].y - ly) < 12) ly = placed[q].y + 12;
        }
        ly = clamp(ly, padT + 6, padT + ph - 5);
        placed.push({ x: px, y: ly });
        if (px + 8 + lw < w - 2) { ctx.textAlign = "left"; ctx.fillText(label, px + 7, ly); }
        else { ctx.textAlign = "right"; ctx.fillText(label, px - 7, ly); }
      }
    }
    if (same) {
      /* park the note in whichever corner the curve is not using: sample the
         curve a quarter of the way across and take the opposite half */
      var uq = xmax * 0.25;
      var vq = byDist ? (S.air ? speedAirAtY(S.lanes[0].vt, uq) : Math.sqrt(2 * G * uq))
                      : (S.air ? speedAir(S.lanes[0].vt, uq) : G * uq);
      var lowLeft = Y(vq) > padT + ph * 0.5;   /* curve still near the floor on the left */
      var note = pw < 300 ? "all three curves overlap" : "all three curves lie on top of each other";
      ctx.font = "600 10px " + MONO; ctx.textAlign = "left"; ctx.textBaseline = "middle";
      var nw = Math.min(ctx.measureText(note).width + 14, pw - 6);
      var nx = lowLeft ? padL + 4 : padL + pw - 4 - nw;
      var ny = lowLeft ? padT + 4 : padT + ph - 22;
      ctx.fillStyle = rgba(C.surface, 0.92);
      ctx.strokeStyle = rgba(C.line, 0.9); ctx.lineWidth = 1;
      ctx.beginPath();
      if (ctx.roundRect) ctx.roundRect(nx, ny, nw, 18, 9); else ctx.rect(nx, ny, nw, 18);
      ctx.fill(); ctx.stroke();
      ctx.fillStyle = rgba(C.muted, 1);
      ctx.fillText(note, nx + 7, ny + 10);
    }
  }

  function draw() { drawTower(); drawChart(); }

  /* ── panels ─────────────────────────────────────────────────────────────── */
  var laneHost = $("lanes");
  function buildLanes() {
    laneHost.innerHTML = "";
    for (var i = 0; i < 3; i++) {
      var d = document.createElement("div");
      d.className = "lane";
      d.innerHTML =
        '<div class="lrow"><i style="background:var(--s' + (i + 1) + ')"></i><b id="ln' + i + '"></b>' +
        '<span class="now" id="lv' + i + '"></span></div>' +
        '<div class="bar"><i id="lb' + i + '" style="background:var(--s' + (i + 1) + ')"></i></div>' +
        '<div class="meta" id="lm' + i + '"></div>';
      laneHost.appendChild(d);
    }
  }

  function sync() {
    var i, L;
    /* clock */
    $("clock").textContent = secs(S.t);
    $("clockSub").textContent = S.state === "replay" ? "replaying the landings"
      : S.state === "done" ? "all three are down" : "since release";
    var wr = $("warp");
    var shown = S.state === "replay" ? REPLAY_RATE : S.state === "falling" ? S.rate : 1;
    wr.textContent = "TIME " + rateTxt(shown);
    wr.setAttribute("data-hot", (S.state === "replay" || shown > 1.8 || shown < 0.7) ? "1" : "0");

    /* status */
    var st = $("status"), stt = $("statusText");
    var label = S.state === "falling" ? "FALLING" : S.state === "paused" ? "PAUSED" :
      S.state === "replay" ? "SLOW-MO" : "LANDED";
    stt.textContent = label;
    st.setAttribute("data-state", (S.state === "falling" || S.state === "replay") ? "run" : "idle");

    /* lanes */
    var order = [0, 1, 2].sort(function (a, b) { return S.lanes[a].tLand - S.lanes[b].tLand; });
    var winner = order[0], spread = S.lanes[order[2]].tLand - S.lanes[order[0]].tLand;
    var tie = spread < 0.02;
    for (i = 0; i < 3; i++) {
      L = S.lanes[i];
      var v = speedAt(L, S.t), landed = S.t >= L.tLand - 1e-9;
      $("ln" + i).textContent = L.o.name;
      $("lv" + i).textContent = sp(v) + " m/s";
      $("lv" + i).style.color = "var(--s" + (i + 1) + ")";
      var frac = S.air ? v / L.vt : v / Math.max(L.vImp, 0.001);
      $("lb" + i).style.width = (clamp(frac, 0, 1) * 100).toFixed(1) + "%";
      var spec = gram(L.o.m) + " · " + areaCm(L.o.a) + " · drag " + L.o.cd.toFixed(2);
      var res;
      if (S.air) {
        res = "terminal <b>" + sp(L.vt) + " m/s</b> · " + (Math.round(clamp(frac, 0, 1) * 100)) + "% of it";
      } else {
        res = "no air · nothing to level off against";
      }
      var land = landed
        ? "landed <b>" + secs(L.tLand) + " s</b> at <b>" + sp(L.vImp) + " m/s</b> (" + kmh(L.vImp) + " km/h)"
        : "lands at " + secs(L.tLand) + " s";
      if (landed && i === winner && !tie) land += " <span class='win'>· first down</span>";
      $("lm" + i).innerHTML = spec + "<br>" + res + "<br>" + land;
    }

    /* result strip */
    var fitEl = $("fit"), fv = $("fitv"), fm = $("fitmsg");
    var allDown = S.t >= tMax() - 1e-9;
    if (!allDown) {
      fitEl.setAttribute("data-ok", "0");
      fv.textContent = secs(tMin()) + " s";
      fm.textContent = "is when the first one touches down. " +
        (S.air ? "Watch each speed stop climbing." : "With no air they cannot come apart.");
    } else if (tie) {
      fitEl.setAttribute("data-ok", "1");
      fv.textContent = "DEAD HEAT";
      fm.textContent = !S.air
        ? "All three land at " + secs(S.lanes[0].tLand) + " s. Nothing pushes back, so mass and shape stop mattering."
        : coincident()
          ? "All three land at " + secs(S.lanes[0].tLand) + " s — same terminal speed, so the same fall."
          : "All three land at " + secs(S.lanes[0].tLand) + " s — different objects, but their terminal speeds land them together.";
    } else {
      fitEl.setAttribute("data-ok", "0");
      fv.textContent = S.lanes[winner].o.name;
      fm.textContent = "lands first at " + secs(S.lanes[winner].tLand) + " s — " +
        S.lanes[order[2]].o.name.toLowerCase() + " needs " + secs(S.lanes[order[2]].tLand) +
        " s, a gap of " + secs(spread) + " s.";
    }

    /* captions + a11y text */
    $("modeTag").textContent = S.air ? "air" : "vacuum";
    $("chartTag").textContent = (S.chartX === "dist" ? "speed vs distance" : "speed vs time") + (S.chartY === "log" ? " · log" : "");
    $("towerCap").innerHTML = S.air
      ? "Dashes mark the release line at <b>" + S.H + " m</b>." +
        (numbersShown ? " Numbers beside each object are its speed right now, in m/s."
                      : " Live speeds are in the readout.")
      : "Vacuum: no air to push back, so every object gains <b>9.81 m/s</b> of speed every second, whatever it weighs.";
    $("chartCap").innerHTML = S.air
      ? "Dashed lines are each object's terminal speed — <b>v = sqrt(2mg / (rho·Cd·A))</b>. The curves bend over and hug them."
      : S.chartX === "time"
        ? "In vacuum the three curves are the same curve: <b>v = g·t</b>, a straight climb that never levels off."
        : "In vacuum the three curves are the same curve: <b>v = sqrt(2g·y)</b> — still climbing when it hits the ground, with nothing to level it off.";
    desc.textContent = "Three objects falling from " + S.H + " metres " + (S.air ? "through air" : "in a vacuum") +
      ". Clock " + secs(S.t) + " seconds. " +
      S.lanes.map(function (L) { return L.o.name + " at " + sp(speedAt(L, S.t)) + " metres per second"; }).join(", ") + ".";
    cdesc.textContent = "Speed curves. " + S.lanes.map(function (L) {
      return L.o.name + (S.air ? ": terminal speed " + sp(L.vt) + " metres per second, " : ": no terminal speed, ") +
        "lands at " + secs(L.tLand) + " seconds hitting " + sp(L.vImp) + " metres per second";
    }).join(". ") + ".";
  }

  function syncButtons() {
    $("pause").textContent = S.state === "paused" ? "Resume" : "Pause";
    $("pause").disabled = !S.animate || (S.state === "done");
    $("replay").disabled = !S.animate || (S.state !== "done" && S.state !== "paused");
    $("mAir").setAttribute("aria-pressed", S.air ? "true" : "false");
    $("mVac").setAttribute("aria-pressed", S.air ? "false" : "true");
    $("airN").textContent = S.air ? "ON" : "OFF";
    $("xDist").setAttribute("aria-pressed", S.chartX === "dist" ? "true" : "false");
    $("xTime").setAttribute("aria-pressed", S.chartX === "time" ? "true" : "false");
    $("yLin").setAttribute("aria-pressed", S.chartY === "lin" ? "true" : "false");
    $("yLog").setAttribute("aria-pressed", S.chartY === "log" ? "true" : "false");
    $("heightN").textContent = S.H + " m";
    var st = Math.max(1, Math.round(S.H / 3.2));
    $("storeys").textContent = "about " + st + (st === 1 ? " storey" : " storeys") + " up";
  }

  /* ── wiring ─────────────────────────────────────────────────────────────── */
  function fillSelects() {
    for (var i = 0; i < 3; i++) {
      var sel = $("obj" + i);
      var html = "";
      for (var k = 0; k < OBJECTS.length; k++) {
        html += '<option value="' + OBJECTS[k].id + '">' + OBJECTS[k].name + "</option>";
      }
      sel.innerHTML = html;
      sel.value = S.ids[i];
      (function (idx, s) {
        s.addEventListener("change", function () { S.ids[idx] = s.value; restart(); });
      })(i, sel);
    }
  }

  $("mAir").addEventListener("click", function () { if (!S.air) { S.air = true; restart(); } });
  $("mVac").addEventListener("click", function () { if (S.air) { S.air = false; restart(); } });
  $("height").addEventListener("input", function () { S.H = parseInt(this.value, 10); restart(true); });
  $("height").addEventListener("change", function () {
    announce("Drop height " + S.H + " metres.");
  });
  $("drop").addEventListener("click", function () { restart(); });
  $("pause").addEventListener("click", function () {
    if (S.state === "falling" || S.state === "replay") { S.paused = S.state; S.state = "paused"; }
    else if (S.state === "paused") { S.state = S.paused || "falling"; kick(); }
    syncButtons(); sync(); draw();
  });
  $("replay").addEventListener("click", startReplay);
  $("anim").addEventListener("change", function () {
    S.animate = this.checked;
    restart();
  });
  $("xDist").addEventListener("click", function () { S.chartX = "dist"; syncButtons(); sync(); draw(); });
  $("xTime").addEventListener("click", function () { S.chartX = "time"; syncButtons(); sync(); draw(); });
  $("yLin").addEventListener("click", function () { S.chartY = "lin"; syncButtons(); sync(); draw(); });
  $("yLog").addEventListener("click", function () { S.chartY = "log"; syncButtons(); sync(); draw(); });

  document.addEventListener("keydown", function (e) {
    var tag = e.target && e.target.tagName;
    if (tag === "INPUT" || tag === "SELECT" || tag === "TEXTAREA") return;
    var k = e.key.toLowerCase();
    if (k === "d") { e.preventDefault(); restart(); }
    else if (k === "v") { e.preventDefault(); S.air = !S.air; restart(); }
    else if (k === "r") { if (!$("replay").disabled) { e.preventDefault(); startReplay(); } }
    else if (k === " " || k === "spacebar") {
      if (tag === "BUTTON") return;
      e.preventDefault(); $("pause").click();
    }
  });

  var rto = 0;
  window.addEventListener("resize", function () {
    if (rto) clearTimeout(rto);
    rto = setTimeout(function () { rto = 0; sync(); draw(); }, 90);
  });
  /* the tower stretches to whatever the side panels need, so its box can change
     without the window changing — repaint on the box, not just on resize */
  if (window.ResizeObserver) {
    var ro = new ResizeObserver(function () {
      var before = numbersShown;
      draw();
      if (before !== numbersShown) sync();   /* only text that actually changed */
    });
    ro.observe(towerCv.parentNode);
    ro.observe(chartCv.parentNode);
  }

  /* ── boot ───────────────────────────────────────────────────────────────── */
  fillSelects();
  buildLanes();
  restart();
})();
</script>
</body>
</html>