Question

A body is dropped from a height of $80$m on to a horizontal floor and impings repeatedly. If it stops in $6$ seconds, the total distance travelled by it before stops is (nearly). $(g=10m{s}^{-2})$.

• A. $86.6$m
• B. $95$m
• C. $100$m
• D. $110$m

Answer 1

The correct option is A $86.6$m

Let the value of coefficient of restitution be $e$.

Initial height of the body $H=80m$

Time taken by the body to reach the ground $t=\sqrt{\frac{2H}{g}}$

$⟹t=\sqrt{\frac{2\times 80}{10}}=4s$

Total time taken by body to stop is given by $T=t(\frac{1+e}{1-e})$

$\therefore 6=4(\frac{1+e}{1-e})$

$⟹e=0.2$

Total distance travelled by body before coming to rest is given by $S=H(\frac{1+e^2}{1-e^2})$

$\therefore$ $S=80(\frac{1+{0.2}^2}{1-{0.2}^2})=86.6m$