Q. 80 Whenever a certain ball is dropp... [FREE SOLUTION]

Chapter 7: Q. 80 (page 616)

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?

Short Answer

Expert verified

The total distance the ball travels before coming to rest when it is dropped from a height of hmeters is $h + \frac{p h}{50} (\frac{100}{100 - p}) .$

Step by step solution

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,

$d = h + 2 脳 h 脳 (\frac{p}{100}) + 2 脳 h 脳 {(\frac{p}{100})}^{2} + . . . d = h + 2 脳 h 脳 \frac{p}{100} (1 + (\frac{p}{100}) + {(\frac{p}{100})}^{2} + . . .) Use the formula of geometric series (\frac{a}{1 - r}) d = h + 2 脳 h 脳 \frac{p}{100} (\frac{1}{1 - \frac{p}{100}}) d = h + \frac{p h}{50} (\frac{100}{100 - p})$

Thus, the total distance traveled by the ball before coming to the rest is $h + \frac{p h}{50} (\frac{100}{100 - p}) .$

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91影视

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?

Short Answer

Step by step solution

Step 1. Given Information.

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

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