A tennis ball bounces on the floor three times, and each time it loses 23.0% of its energy due to heating. How high does it bounce after the third time, if we released it $4.0 \mathrm {~m}$ from the floor?

Question

Quizplus · Accepted Answer

The ball loses 23% of its energy each time it bounces. After the first bounce, it has 77% of its original energy. After the second bounce, it has 77% of 77%, or 59.29% of its original energy. After the third bounce, it has 59.29% of 59.29%, or 35.15% of its original energy.The height to which the ball bounces is proportional to its energy. So, after the third bounce, the ball will bounce to 35.15% of its original height. Since it was released from a height of 4.0 m, it will bounce to a height of 0.3515 * 4.0 m = 1.406 m = 140.6 cm.

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