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A tennis ball bounces on the floor three times. If each time it loses 22.0% of its energy due to heating, how high does it rise after the third bounce, provided we released it 2.3 m from the floor?

A tennis ball bounces on the floor three times. If each time it loses 22.0% of its energy due to heating, how high does it rise after the third bounce, provided we released it 2.3 m from the floor?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:** A tennis ball bounces on the floor three times. If each time it loses 22.0% of its energy due to heating, how high does it rise after the third bounce, provided we released it 2.3 m from the floor? **Explanation:** The problem involves calculating the height a tennis ball reaches after multiple bounces, accounting for energy loss at each bounce. Initially, the ball is released from a height of 2.3 meters. With each bounce, the ball loses 22.0% of its energy due to heating. The task is to determine the height reached by the ball after the third bounce. **Concepts Involved:** - **Energy Loss**: After each bounce, the ball retains 78.0% (100% - 22.0%) of its energy. - **Height Calculation**: The height after each bounce can be computed by multiplying the previous height by 0.78 (78% energy retention). **Steps to Solve:** 1. **Initial Release Height**: 2.3 m. 2. **First Bounce**: - Energy retained: 78% - New height = 2.3 m × 0.78 = 1.794 m 3. **Second Bounce**: - Energy retained: 78% - New height = 1.794 m × 0.78 = 1.39932 m 4. **Third Bounce**: - Energy retained: 78% - New height = 1.39932 m × 0.78 = 1.0914 m After the third bounce, the tennis ball rises approximately 1.09 meters from the floor.
Transcribed Image Text:**Problem Statement:** A tennis ball bounces on the floor three times. If each time it loses 22.0% of its energy due to heating, how high does it rise after the third bounce, provided we released it 2.3 m from the floor? **Explanation:** The problem involves calculating the height a tennis ball reaches after multiple bounces, accounting for energy loss at each bounce. Initially, the ball is released from a height of 2.3 meters. With each bounce, the ball loses 22.0% of its energy due to heating. The task is to determine the height reached by the ball after the third bounce. **Concepts Involved:** - **Energy Loss**: After each bounce, the ball retains 78.0% (100% - 22.0%) of its energy. - **Height Calculation**: The height after each bounce can be computed by multiplying the previous height by 0.78 (78% energy retention). **Steps to Solve:** 1. **Initial Release Height**: 2.3 m. 2. **First Bounce**: - Energy retained: 78% - New height = 2.3 m × 0.78 = 1.794 m 3. **Second Bounce**: - Energy retained: 78% - New height = 1.794 m × 0.78 = 1.39932 m 4. **Third Bounce**: - Energy retained: 78% - New height = 1.39932 m × 0.78 = 1.0914 m After the third bounce, the tennis ball rises approximately 1.09 meters from the floor.
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