When the balls are dropped together, both have a downward velocity "v" just before striking the floor. The larger bottom ball reverses its velocity an instant before the top ball. The smaller top ball is still moving downward when it strikes the larger ball which is now moving upwards.

     The bottom ball acts like a moving wall. Before the balls collide, their velocity becomes 2v, twice that of their original speed. After the balls collide, the small ball has a velocity of 2v plus v (the larger balls original velocity) which gives it an overall velocity of 3v. This is because the velocity of the small ball is tripled after impact. It will then bounce 9 times its original height.

     This can be proved by the equation v² = 2gy.

     If you want to add even more bounce, try doing this with 3 balls. Have the top ball be very light (such as a ping pong ball) and the bottom one heavy. You will find that the top ball bounces back 49 times its height!