Question

After striking the floor ball rebounds ${\frac{4}{5}}^{\text{th}}$ of its height from which it has fallen. If it is released from a height of $120$m, then the total distance travelled by the ball (in $\text{m}$) before it comes to rest is

• A. $960$
• B. $1000$
• C. $1080$
• D. $2040$

Answer 1

The correct option is C $1080$

Except the first fall, the ball will travel the same distance twice (upward and downward) in each step.
Total distance $=h+2[\frac{4h}{5}+\frac{4^{2}h}{5^2}+\cdots ]$
$=120+2[120\times \frac{4}{5}+120\times {\left(\frac{4}{5}\right)}^2+120\times {\left(\frac{4}{5}\right)}^3+...]$
$=120+240[\frac{4}{5}+{\left(\frac{4}{5}\right)}^2+{\left(\frac{4}{5}\right)}^3+...]$
$=120+240\left[\frac{\frac{4}{5}}{1-\frac{4}{5}}\right]=120+960=1080\text{m}$