Chapter 11.6, Problem 8P

To determine

To find:

The total vertical distance traveled by the bell before it stops bouncing.

Answer to Problem 8P

  $300$

Explanation of Solution

Given:

A geometric series with ratio $0.95$ .

Concept used:

General form is

  $\left(h-a,k\right)and\left(h+a,k\right)$

The general form an ellipse with horizontal major axis

  $\frac{{\left(x-h\right)}^2}{a^2}+\frac{{\left(y-k\right)}^2}{b^2}$

Calculation:

The ball was thrown to a height of $10m$

Initial element $=20$

  $\begin{array}{l}=20{\displaystyle \sum _{k=0}^{\infty }{\left(0.95\right)}^k}\\ =\frac{20}{0.05}\\ =400\end{array}$

Substract the initial $10m$

Since the ball was dropped from $10m$

  $\begin{array}{l}=400-10\\ =300\end{array}$

Therefore, The total vertical distance traveled by the bell before it stops bouncing is $300$ .