   Chapter 13.3, Problem 97E ### 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 A certain ball rebounds to half the height for 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 the rest.

To determine

To find:

The total distance that the ball travels.

Explanation

Given:

The ball bounces to half the height h=1m form which it is dropped.

Approach:

The sum of the infinite geometric series is given by S=a1r;|r|<1.

Calculation:

When the ball hits the ground for the first time, it has traveled a distance d1=1m and the distance traveled up and down for the second time is d2=12m, it will travel 12m twice when up and down and similarly, it will be the half of the previous distance for further bounces.

Form a sequence-

1,12,14,18,...

The total distance for infinite times, written as-

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