Question

Celeste drops a basketball (0.9 kg) from a height of 5 m above the ground.  If the ball loses 25 % of its total energy as it bounces back up, to what maximum height will it rebound?

Answer 1

So, as the ball rebounds, it still contain 100-25-75% of its initial energy. Find the initial energy:

$$E_i=mgh$$

Therefore, the final energy is

$$E_f=mgy=0.75E_i=0.75mgh.\\\space\\ y=\frac{0.75mgh}{mh}=0.75h=3.75\text{ m}.$$