Question

A ball is dropped onto a fixed horizontal surface from height h₀. The coefficient of restitution is ‘e’. The total distance ‘D’ travelled by ball before it comes to rest on the surface.

• A. $\left(\frac{1-e^2}{1+e^2}\right).h_0$
• B. $\left(\frac{1+e^2}{1-e^2}\right).h_0$
• C. $\left(\frac{1+e}{1-e}\right).h_0$
• D. $\left(\frac{1+e^2}{1-e^2}\right).h_0$

Answer 1

The correct option is D $\left(\frac{1+e^2}{1-e^2}\right).h_0$

$e=\sqrt{\frac{h_i}{h_{i-1}}}\Rightarrow e^{2n}=\frac{h_n}{h_o}or{h}_n=e^{2n}.h_{o}Now,D=h_o+2(h_1+h_2+h_3+----=h_o+2(e^2.h_o+e^4.h_o+e^6.h_o+----)=h_o(\frac{1+e^2}{1-e^2})$