A tennis ball bounces on the floor three times,and during each bounce 23% of its kinetic energy (assuming that at the collision with the floor the ball-Earth system only had kinetic energy)is converted to internal energy..How high does it go after the third bounce,if we released it 4.0 m from the floor?

Question

Quizplus · Accepted Answer

After each bounce, the ball retains 77% (100% - 23%) of its kinetic energy due to the conversion of 23% of its kinetic energy to internal energy. After three bounces, the kinetic energy retained by the ball is $0.77^3$ of its initial kinetic energy. The height to which the ball rises is directly proportional to its kinetic energy at the point of rebound. Therefore, after three bounces, the height reached by the ball is $0.77^3 \times 4.0 \, \text{m} = 0.456533 \times 4.0 \, \text{m} = 1.826132 \, \text{m}$, which is approximately 180 cm.

A Tennis Ball Bounces on the Floor Three Times,and During