Energy Efficiency?

Question

A 5.32 kg ball hits the floor and bounces back up. Just before it hits the floor its velocity is v=9.97 m/s in the vertical direction.
What is the maximum height the ball can rebound to?

Answer 1

Assuming a perfectly elastic collision with the floor (i.e. no energy is lost due to deforming the ball, the floor, etc.), the ball must return to the height where its speed is zero. At that height above teh floor, the ball's potential energy will be equal to the ball's kinectic energy just before it struck the floor.

So KE = PE --> 1/2mv^2 = mgh

or solving for h;

h = 1/2 v^2/g =0.5*(9.97 m/s)^2/(9.8m/s^2) = 5.07 m