Chapter MPS, Problem 11.4MPS

a.

To determine

To find how high the ball will bounce on its sixth bounce.

Answer to Problem 11.4MPS

  $23.5$ Feet.

Explanation of Solution

Given:

The ball is dropped from $200$ feet and it recovers $70\%$ of its height. After the second bound it reaches $98$ feet.

Calculation:

The situation is clearly an example of geometric sequence.

Here,

  $\begin{array}{l}{a}_1=200\times 0.7=140\\ a_2=140\times 0.7=98\\ \mathrm{.......}\\ $ a_7=a{r}^6=200{(0.7)}^6=23.5298$\end{array}$

Therefore, the approximate height of the ball on its sixth bounce is $23.5$ feet.

b.

To determine

To find the sum of heights the ball has bounced through on its sixth bounce.

Answer to Problem 11.4MPS

  $411.8$ Feet.

Explanation of Solution

Given:

The ball is dropped from $200$ feet and it recovers $70\%$ of its height. After the second bound it reaches $98$ feet.

Calculation:

The situation is clearly an example of geometric sequence.

Here,

  $a_1=140,r=0.7$

The sum of first seven terms of GP are-

  $S_6=\frac{a(1-r^n)}{1-r}=\frac{140(1-{(0.7)}^6)}{1-0.7}=411.7638$

Therefore, the sum of heights the ball has bounced through on its sixth bounce is $411.8$ feet.