Question

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

• A. $1080$ metre
• B. $1180$ metre
• C. $1160$ metre
• D. $1260$ metre

Answer 1

The correct option is A $1080$ metre

Total distance is
$S=120+120\times \frac{4}{5}\times 2+120\times {\left(\frac{4}{5}\right)}^2\times 2+120\times {\left(\frac{4}{5}\right)}^3\times 2+...$
$\Rightarrow S=120+240\times \frac{4}{5}+240\times {\left(\frac{4}{5}\right)}^2+....$
$\Rightarrow S=120+240\times \frac{4}{5}(1+\frac{4}{5}+{\left(\frac{4}{5}\right)}^2+...)$
$\Rightarrow S=120+240\times \frac{4}{5}\times \frac{1}{1-\frac{4}{5}}=120+48\times 4\times 5=1080$