Approximately how many rebounds will the ball make before losing 93% of its energy?

Question

A ball is dropped from a height of 1.50 m and rebounds to a height of 1.25 m .

Answer 1

Starting energy is potential energy = mgh = 1.5mg

After losing 93% of its energy, it will be .07(1.5)mg = .105mg

Let B = number of bounces

energy after bounce 1 = 1.5(.833)mg = 1.25mg

bounce 2 = 1.5(.833)(.833)mg = 1.5(.833)²mg

So

Energy = 1.5(.833)^Bmg

Let's solve for B: 1.5(.833)^Bmg = .105mg B = 14.59 or 15 bounces