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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

Bouncing Ball A ball is dropped from a height of 9 ft . The elasticity of the ball is such that it always bounces up one third the distance it has fallen.

( a ) Find the total distance the boll has traveled at the instant it hits the ground the fifth time.

( b ) Find a formula for the total distance the ball has traveled at the instant it hits the ground the n t h time.

To determine

(a)

To find:

The total distance traveled by the ball when it hits the ground for the fifth time.

Explanation

Given:

The ball is fallen from a height of 9ft, the ball bounces up one third the distance it has fallen.

Approach:(1) The nth partial sum of the geometric series is Sn=arn1r1r1.

Calculation:

When the ball hits the ground for the first time, it has traveled a distance d1=9ft and the distance traveled up and down for the second time is d2=3ft, it will travel 3ft twice when up and down and similarly, it will be the one third of the previous distance for further bounces

Form a sequence-

9,3,1,13,19,...

Here, a=9, r=13

The total distance D for the fifth time can be written in the form-

To determine

(b)

To find:

Formula for the total distance for the nth time.

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