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Q. 80

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Calculus
Found in: Page 616
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Whenever a certain ball is dropped, it always rebounds to a height p% (0 < p < 100) of its original position. What is the total distance the ball travels before coming to rest when it is dropped from a height of h meters?

The total distance the ball travels before coming to rest when it is dropped from a height of h meters is h+ph50100100-p.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Given Information. 

The ball after dropping rebounds to a height p% (0 < p < 100) of its original position.

Step 2. Find the distance the ball travels before coming to rest when it is dropped from a height of h meters. 

To find the total distance traveled by the ball, let's first find the distance traveled by the ball before coming to rest, each successive bounce has two times p% of the height as it involves up and down of the ball,

d=h+2×h×p100+2×h×p1002+...d=h+2×h×p1001+p100+p1002+...Use the formula of geometric seriesa1-rd=h+2×h×p10011-p100d=h+ph50100100-p

Thus, the total distance traveled by the ball before coming to the rest is h+ph50100100-p.

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