Question

A ball is dropped from a height of $3m$. If coefficient of restitution between the surface and ball is $0.5$, then the total distance covered by the ball before it comes to rest is

• A. 3 m
• B. 4 m
• C. 5 m
• D. 6 m

Answer 1

Answer: (C)

5 m

If a ball dropped from height $h_1$ then it bounces back to $h_2$ then
$h_2=e^2{h}_1$
similarly for again falling from height $h_2$
$h_3=e^2{h}_2$
$h_3=e^4{h}_1$
total distance$=h_1+2h_2+2h_3+............$
total distance $=3+2e^2\times 3+2e^4\times 3............$
$=-3+6(1+e^2+e^4..............)$
$=-3+\frac{6}{1-e^2}$
$=-3+\frac{6}{0.75}$
$=5$ m