Question

A particle falls from a height ${}^{\prime }{h}^{\prime }$ upon a fixed horizontal plane and rebounds. If ${}^{\prime }{e}^{\prime }$ is the coefficient of restitution, the total distance travelled before it comes to rest is

• A. $h\left(\frac{1+e^2}{1-e^2}\right)$
• B. $h\left(\frac{1-e^2}{1+e^2}\right)$
• C. $\frac{H}{2}\left(\frac{1-e^2}{1+e^2}\right)$
• D. $\frac{H}{2}\left(\frac{1+e^2}{1-e^2}\right)$

Answer 1

Answer: (A)

$h\left(\frac{1+e^2}{1-e^2}\right)$

Total distance $=h+2\times e^2\times h+2\times e^4\times h.............$
$=-h+2h(1+e^2..........)$

$=-h+\frac{2h}{1-e^2}$

$=h\left(\frac{1+e^2}{1-e^2}\right)$