Chapter 8, Problem 6CA

To determine

Find the comparison between the total distance traveled by the basketball and the baseball.

Answer to Problem 6CA

The total distance traveled by the basketball is $2.68\text{ft}\text{.}$ greater than the baseball distance.

Explanation of Solution

Given:

The given diagram is

  

Basketball and a baseball dropped from a height of $10$ feet.

Calculation:

For the basketball, use geometric series sum formula $\frac{a_1}{1-r}$ .

  $\begin{array}{l}{a}_1=10\\ r=0.36\end{array}$

Sum $=2\left(\frac{a_1}{1-r}\right)-10$

  $\begin{array}{l}=2\left(\frac{10}{1-0.36}\right)-10\\ =2\left(\frac{10}{0.64}\right)-10\\ =31.25-10\\ =21.25\end{array}$

For the baseball, use geometric series sum formula $\frac{a_1}{1-r}$ .

  $\begin{array}{l}{a}_1=10\\ r=0.30\end{array}$

Sum $=2\left(\frac{a_1}{1-r}\right)-10$

  $\begin{array}{l}=2\left(\frac{10}{1-0.30}\right)-10\\ =2\left(\frac{10}{0.70}\right)-10\\ =28.57-10\\ =18.57\end{array}$

Find the difference between the total distance traveled by the basketball and the baseball.

  $\begin{array}{l}=21.25-18.57\\ =2.68\text{ft}\text{.}\end{array}$

Hence the total distance traveled by the basketball is $2.68\text{ft}\text{.}$ greater than the baseball distance.