Chapter 7, Problem 1TP

Solution

To identify: The difference by which the total distance traveled by the basketball is more than the total distance traveled by the baseball if the baseball and basketball dropped from the height of 10 feet. On each bounce, the basketball bounces to 36 percent of its previous height and the baseball bounces to 30 percent of its previous height.

  

The options are:

  $\left(a\right)1.34\text{feet}$

  $\left(b\right)2.00\text{feet}$

  $\left(c\right)2.62\text{feet}$

  $\left(d\right)5.63\text{feet}$

The correct option is $\left(a\right)1.34\text{feet}$ .

Given information:

A baseball and a basketball dropped from the height of 10 feet. On each bounce, the basketball bounces to 36 percent of its previous height and the baseball bounces to 30 percent of its previous height.

The given diagram is:

  

Explanation:

Consider the given diagram,

  

A basketball dropped from the height of 10 feet. On each bounce, the basketball bounces to 36 percent of its previous height.

Then the first term will become $a_1=10$ and the common ratio will be $r=0.36$ .

As $\left|r\right|<1$ then the total distance traveled by the basketball is: $S_{basketball}=\frac{a_1}{1-r}$

  $\begin{array}{c}{S}_{basketball}=\frac{10}{1-0.36}\\ =\frac{10}{0.64}\\ =15.625\end{array}$

Similarly, a baseball dropped from the height of 10 feet. On each bounce, the basketball bounces to 30 percent of its previous height.

Then the first term will become $b_1=10$ and the common ratio will be $r=0.30$ .

As $\left|r\right|<1$ then the total distance traveled by the basketball is: $S_{baseball}=\frac{b_1}{1-r}$

  $\begin{array}{c}{S}_{baseball}=\frac{10}{1-0.30}\\ =\frac{10}{0.70}\\ =14.286\end{array}$

The difference between the distance traveled by the basketball and the baseball is:

  $\begin{array}{c}{S}_{basketball}-S_{baseball}=15.625-14286\\ \approx 1.34\end{array}$

Thus the total distance traveled by the basketball is 1.34 feet greater than the distance traveled by the baseball. Option $\left(a\right)1.34\text{feet}$ should be the correct option.