   Chapter 13.3, Problem 98E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Bouncing Ball If the ball in Exercise 97 is dropped from a height of 8 ft, then 1 s is required for its first complete bounce − from the instant it first touches the ground until it next touches the ground. Each subsequent complete bounce requires 1 / 2 as long as the preceding complete bounce. Use an infinite geometric series to estimate the time interval from the instant the ball first touches the ground until it stops bouncing.97. Bouncing Ball A certain ball rebounds to half the height from which it is dropped. Use an infinite geometric series to approximate the total distance the ball travels after being dropped from 1 m above the ground until it comes to rest.

To determine

To find:

Estimation of the time interval from the instant the ball first touches the ground until it stop bouncing.

Explanation

Given:

A ball requires 1s to complete its first bounce when dropped from a height of 8 ft and subsequent complete bounce requires 12 as long as the preceding complete bounce. This process continues until the ball stops bouncing.

Approach:

Let T1,T2,T3,... be the time taken by the ball to complete its first bounce, second bounce, third bounce and so on.

Since, the next bounce requires 12 as long as the preceding complete bounce.

T1=1s, T2=12s, T3=12(12)s and so on.

Clearly, T1,T2,T3,

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