Approximately how many rebounds will the ball make before losing 90% of its energy?

Question

A ball is dropeed from a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?

Answer 1

The energy of the ball is equivalent to the potential energy at the top of each bounce. The first bounce indicates that the ball's energy is 1.20/1.50 = 0.80 after each bounce.
We need to solve 0.80^n = 0.10 for n
n= log(0.10)/log(0.80) = 10.31.
Therefore about the ball loses about 90% of its energy in 10 bounces.

Answer 2

Four and a half times.