Question

After striking the floor a certain ball rebounds $\frac{4}{5}\text{th}$ of its height from which it has fallen. The total distance that the ball travels before coming to rest if it is gently released from a height of $120m$ is

• A. 960 m
• B. 1000 m
• C. 1080 m
• D. Infinite

Answer 1

Answer: (C)

Initially, the ball falls from a height of $120m$.
After striking the floor, it rebounds and goes to a height of $\frac{4}{5}\times (120)m$.
Now, it falls from a height of $\frac{4}{5}\times (120)m$ and after rebounding goes to a height of $\frac{4}{5}\left(\frac{4}{5}(120)\right)m$.
This process is continued till the ball comes to rest.
Hence, the total distance travelled is
$D=120+2\left[\frac{4}{5}(120)+{\left(\frac{4}{5}\right)}^2(120)+\dots \infty \right]$
The above series in brackets is an infinte $GP$,
$\therefore D=120+2\left[\frac{\frac{4}{5}(120)}{1-\frac{4}{5}}\right]$
$=120+2\left[\frac{480}{1}\right]=1080m$