Question

A girl throws a ball an initial velocity v at an angle of ${45}^{\circ }$. The ball strikes a smooth vertical wall at a horizontal distance d from the girl and after rebound returns to her hands. What is the coefficient of restitution between wall and ball? $(v^2>dg)$

• A. $\frac{v^2-gd}{gd}$
• B. $\frac{gd}{v^2-gd}$
• C. $\frac{gd}{v^2}$
• D. $\frac{v^2}{gd}$

Answer 1

The correct option is B $\frac{gd}{v^2-gd}$

$t_1+t_2=2V\frac{sin{45}^{\circ }}{g}$

$\frac{d}{vcos{45}^{\circ }}+\frac{d}{evcos{45}^{\circ }}=\frac{2vsin{45}^{\circ }}{g}$

$\Rightarrow e=\frac{gd}{v^2-gd}$