Question

A ball is dropped from rest at the top of a 5.89-m-tall building, falls straight downward, collides inelastically with the ground, and bounces back. The ball loses 5.34% of its kinetic energy every time it collides with the ground. How many bounces can the ball make and still reach a windowsill that is 2.79 m above the ground?

Answer 1

potential energy proportional to height, m g H
so
Hn = (1-.0534)Hn-1
Hfinal = .9466^n Hinitial
2.79 = .9466^n 5.89
.9466^n = .4737
n log .9466 = log .4737
n = 13.6 so 13

Answer 2

Thanks a lot Damon!