It's a matter of conversion of potential energy energy into kinetic energy and vice versa. The higher the drop distance, the more potential energy the ball has. As it falls the potential energy is transferred into kinetic energy. When the ball hits the floor the ball is squeezed transferring the kinetic energy back into potential energy, like in a spring. Then the ball rebounds, although with a slightly lower velocity due to slight energy loss, and bounces back up losing its vertical kinetic energy back into potential energy.
So, the higher you drop the ball from, the more potential energy it has --> the more kinetic energy it has when it hits the floor --> the higher it bounces back up.
Some of the kinetic energy of the ball is lost during the collision with the floor and the ball will not return to the original height. According to the USTA regulations ball is tested for bounce by dropping it from a height of 100 inches (2.54 m) onto concrete
; a bounce between 53 and 58 inches (1.3462 - 1.4732 m) is acceptable
One problem; the linear relation between drop height and rebound height doesn't work if the height is too large. The reason is that air resistance will slow the ball down and cause it to lose kinetic energy.
(published on 07/25/11)