Count the bounces.

The coefficient of restitution e is the ratio of rebound speed to impact speed, which shows up as a height ratio, e = √(h₁/h₀), because both scale as the square root of height. It's a property of the ball and the surface together, not the ball alone — the values above combine both into one approximate number, so treat them as representative rather than exact (basketball and tennis-on-concrete are close to real regulation figures: the NBA specifies a basketball dropped from 6 ft onto hardwood should rebound 49–54 in, and the ITF specifies a tennis ball dropped from 100 in onto concrete should rebound 53–58 in; the rest are rough estimates). The animation stops once a bounce's predicted peak falls below the ball's own radius — past that point there's no visible bounce left to see, only a sound if something amplifies it, which is what the balloon-drum toggle is for: turn it on and every impact rings the floor, so you can keep counting well past the point your eyes gave up. The total elapsed time shown is the idealized sum of a geometric series — infinitely many bounces in finite time — and a real ball stops a little sooner than that, since rolling, air drag, and sideways drift all bleed away a bit more energy than this model accounts for.