Rebound Height of a Bouncing Ball

Is it possible to determine the rebound/return height bounce for the first bounce of a ball based upon it's gravitational potential energy. In other words, can I find the height of a rebound bounce from the Mass, Gravitational Force and Height it was dropped from?
- Alia Winchester (age 15)
Forest Glen, QLD, Australia

No    You need addtional information related to how much energy was dissipated during the contact with the floor.  You can see this by considering a thought experiment:  imagine dropping balls of different materials, but all from the same original height.

If we assume a perfectly elastic interaction, then the ball bounces back up to the original height.  Some rubber balls get close to this.    A "perfectly plastic" interaction dissipates the maximum possible energy and the rebound height is zero; think of dropping a lump of wet clay.

The effect is sometimes quanitifed by the notion of "coefficient of restitution"

(published on 03/20/2016)