Projectile Playground

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. The gap between them is the whole story.

A slingshot launching balls at a bucket, with flight paths drawn. Your browser does not support canvas.
drag the ball back to aim — or use the sliders
with air no air
Click the field, then ← → angle, ↑ ↓ power, Enter to launch.

Paths kept

    Tap a path to load its settings back into the sliders.

    What’s going on

    Gravity pulls down by the same amount no matter how fast you are going. Air doesn’t: its push grows with speed squared, 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.

    It also moves the sweet spot. In still vacuum the farthest throw is at 45°. Add air and the best angle drops — around 40° for a tennis ball, and near 24° for a beach ball, which spends so long fighting the air that a high, slow arc is simply wasted time.

    Try the steel ball: 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.

    This shot

    no air
    with air
    Distance
    —
    —
    Peak height
    —
    —
    Time in air
    —
    —
    Landing speed
    —
    —
    loaded — ready to launch
    Bucket sits at—
    Best angle now—

    Air is taking a bite out of this shot.

    Aim

    45°
    24.0 m/s
    38 m

    Ball

    Weight & size—
    Drag factor—

    Drag factor is ½·ρ·C·A ÷ m — how much air the ball has to shove aside for every gram it carries. A beach ball is nearly all sail and no mass.