Question

After striking a floor a certain ball rebounds 4/5th of the height from which it has fallen. Let the total distance that it travels before coming to rest be k, when it is gently dropped from a height of 120 metres.Find $k/120$ ?

Answer 1

If the ball is dropped from a height $h$, distance travelled by it looks like $h+\frac{4h}{5}$(while it goes up) + $\frac{4h}{5}$(while it comes down) $+(\frac{4}{5}{)}^{2}h+(\frac{4}{5}{)}^{2}h+$.... infinite times
Using the formula for infinite geometric progression, the sum becomes $h+2\left[\frac{\frac{4h}{5}}{1-\frac{4}{5}}\right]=9h$
Here, $k=9h$ and $h$ is given to be $120.$
$\Rightarrow \frac{k}{120}=9$