Hold a basketball with a tennis ball resting on top. Let go. The basketball hits the floor, and the tennis ball does something that looks like cheating: it shoots up far higher than the height you dropped it from. Nothing was added. Nothing was hidden. It is a two-step bounce, and the second step borrows from the first.
Everything here is ideal point-like balls in a straight vertical line. Each ball is lighter than the one below by the factor you choose. Press Drop, then change the stack and drop again.
The view zooms out as the top ball climbs. The dashed line is the height you dropped from.
Just before landing, both balls fall at the same speed, call it v. Then the floor reverses the big ball: it now moves up at v while the small ball is still coming down at v. In the next instant they meet head on, closing at 2v.
A bouncy collision sends the two apart at the same closing speed. If the lower ball is much heavier, it barely changes speed, so it carries on upward at about v. For the light ball to leave at 2v faster than the big one, it must end up moving at about v + 2v = 3v, upward.
Height grows with the square of launch speed, so tripling the speed multiplies the height by nine. That is the ideal limit with a huge mass ratio and perfect bounce. Drag the ratio towards 30 and the bounciness to 1.00 and the readout should creep towards 9.
The exact outcome for any two masses, big M and small m, is that the small ball leaves at v(3M − m)/(M + m). With equal masses that is just v: they swap speeds like a Newton's cradle, and nothing special happens.
The small ball gains energy, so something must lose it. That something is the big ball: after handing over a sliver of its motion, it comes back to about the same speed as the incoming ball, but a touch slower. Because it is heavy, a tiny drop in its speed is a lot of energy, and the light ball takes it. Total energy never goes up, which you can check: set the bounciness below 1.00 and the peak falls well short of the ideal.
Switch to three balls. Now the middle ball gets launched at 3v into the top ball, which was still coming down. The same trick repeats one level up: relative to the middle ball's upward motion, the top ball is approaching at 4v, and it leaves at up to 7v. Its peak is up to 49 times the drop height. Each extra ball in the ideal limit takes the top speed from 2n − 1 times the impact speed, with n the number of balls in the stack, so the heights go 1, 9, 49 for one, two and three balls.
Real balls squash and warm up when they hit, so they are never perfectly bouncy. The masses are never extreme, and in real stacks the collisions are not perfectly separated in time. The bounce still happens: a tennis ball on a basketball really does fly well above its drop height, just not nine times higher. Try bounciness 0.7 and a ratio of 8 on the simulator for a taste of how fast the gain fades.
The lesson reaches beyond toys. A spacecraft can steal momentum from a planet it passes, and speeds in a collision chain can add. In each case a heavy object loses a hardly noticeable bit of its speed and a light one gets a lot of it.