Question

After striking the floor, a certain ball rebounds ${\left(4/5\right)}^{th}$ of height from which it has fallen. Then the total distance that it travels before coming to rest, if it is gently dropped from a height of 120 m is

• A. 1260 m
• B. 600 m
• C. 1080 m
• D. none of these

Answer 1

The correct option is C 1080 m

Initially, the ball falls from a height of $120m$.

After striking the floor, it rebounds and goes to a height of $\frac{4}{5}\times \left(120\right)m$.

Now, it falls from a height of $\frac{4}{5}\times \left(120\right)m$ and after rebounding goes to a height of $\frac{4}{5}\left(\frac{4}{5}\right(120\left)\right)m$.

This process is continued till the ball comes to rest.

Hence, the total distance travelled is

$D=120+2\left[\frac{4}{5}\right(120)+{\left(\frac{4}{5}\right)}^2(120)+\dots \infty ]$

The above series in brackets is an infinte GP,

$\therefore D=120+2\left[\frac{\frac{4}{5}\left(120\right)}{1-\frac{4}{5}}\right]=120+2\left[\frac{480}{1}\right]=1080m$