Chapter 1, Problem 74A

Interpretation Introduction

Interpretation : The distance bounced by the ball for the third time is to be calculated.

Concept Introduction : The methods for solving numerical problems are arranged into a three-step approach to problem-solving. Analyzing, calculating, and evaluating are the steps in solving a numerical word problem.

Answer to Problem 74A

The total distance the ball has traveled when it hits the ground for the third time is $\text{150}\text{inches}$ .

Explanation of Solution

The ball drops at the height of 60 inches and bounces at the height of 30 inches.

Each time the ball bounces half the distance of its height.

For the first time, the ball drops at a height of 60 inches and bounces at 30 inches.

For the second time, the ball drops at a height of 30 inches and bounces at 15 inches.

For the third time, the ball just drops at a height of 15 inches. Since only till the third time it is asked, the bouncing of the ball after hitting the third time is not taken into account.

To calculate the total distance the ball has traveled when it hits the ground for the third time, add on all the heights and bouncing heights till the third time.

  $\begin{array}{c}\text{distance}\text{=}\left(\text{60}\text{+}\text{30}\text{+}\text{30}\text{+}\text{15}\text{+}\text{15}\right)\text{inches}\\ \text{=150}\text{inches}\end{array}$

The total distance the ball has traveled when it hits the ground for the third time is $\text{150}\text{inches}$ .