Squash balls (and almost all balls) will bounce back higher if they are dropped from a greater height. The kinetic energy of a squash ball just before it hits the ground is directly proportional to the height from which it is dropped. For a superball, with little energy loss in the bounce, the ball rebounds with the same speed upwards after the bounce that it had going downwards before the bounce. Balls that arenít quite so bouncy lose a fraction of their kinetic energy when they collide with the ground, and this fraction doesnít change much with the height from which they are dropped. Even a superball loses a little bit of energy each time it hits the ground. So each bounce will be a little lower than the previous one. If the height from which the ball is dropped is h, then the bounce height will be f*h, where f is the fraction of kinetic energy the ball keeps after bouncing, and 0 < f < 1, with f=0 meaning not bouncy at all, and f=1 meaning very very bouncy. The next bounce will go up to f*f*h, and the third f*f*f*h, and so on. For example. If the ball started at 1m height and first bounce went to 0.9 m, the next would go to 0.81 m, then 0.729 m, etc
As you probably have noticed, squash balls arenít very bouncy at all. They deform when they hit a wall or the floor, and a lot of the energy gets converted to heat during the collision. Squash balls heat up over the course of a game. Either the air in them gets pressurized, or the rubber just gets more flexible, but a squash ball will get more bouncy (larger f) as it heats up.
People who are good at squash have to adjust their playing as a game progresses and the ball heats up! I suspect a basketball will also bounce better if it is hot, but I havenít done the experiment.
(published on 10/22/2007)