Kinematics problem???

Question

A bouncy ball has the property that if it hits the ground with velocity v, it bounces back up with velocity - .8v. If such a ball is dropped from a height h above the ground, how high will it bounce?

Answer 1

It is dropped from height h.

v^2 = 2gh

Or, v = sqrt(2gh)

It bounces with velocity -.8v = -.8 * sqrt(2gh)

Let it bounce to height h2.

Then h = {-.8 * sqrt(2gh)}^2/(2g)

= 0.64 * 2gh/(2g)

= 0.64h

Ans: 0.64h