Chapter MPS, Problem 11.5MPS

To determine

Find the tolat distance travelled by the ball.

Answer to Problem 11.5MPS

  $30meters.$

Explanation of Solution

Given information:

A ball is dropped from a height of $10meters$ . It rebounds one half the distances after each fall.

Calculation:

Consider the height of $10meters$ .

Assume tolat distance travelled by the ball is $d$ .

After travel $10meters$ ,It rebounds one half the distances after each fall,

The ball will travel $5meters$ and $5meters$ downward, then It rebounds one half the distances.

The ball will travel $2.5meters$ and $2.5meters$ downward.

The series will formed,

  $\begin{array}{l}d=10+\left(\frac{10}{2}+\frac{10}{2}\right)+\left(\frac{10}{2^2}+\frac{10}{2^2}\right)+\left(\frac{10}{2^3}+\frac{10}{2^3}\right)+\mathrm{....}\\ d=10+\left(\frac{20}{2}\right)+\left(\frac{20}{2^2}\right)+\left(\frac{20}{2^3}\right)+\mathrm{....}\\ d=10+20\times \left(\frac{1}{2}\right)+\left(\frac{1}{2^2}\right)+\left(\frac{1}{2^3}\right)+\mathrm{....}\end{array}$

The formed series a infinite geometric series with common ratio $\frac{1}{2}$

Now, apply formula,

  $\begin{array}{l}S=\frac{a}{1-r}\\ S=\frac{1/2}{1-1/2}\\ S=1\\ d=10+20\times 1\\ =30meters.\end{array}$

Hence, total distance travelled by the ball is $30meters.$