Question

A ball is projected from a point in one of the two smooth parallel vertical walls against the other in a plane perpendicular to both. After being reflected at each wall impinge again on the second at a point in the same plane as it started. The distance between two walls is $a.b$ is the free range and $e$ be the coefficient of restitution:

• A. The total time taken in moving from $O$ to $C$ is $\frac{a}{e^{2}u}(e^2+e+1)$
• B. The free range on the horizontal plane $b=\frac{2uv}{g}$
• C. $b{e}^2=a(e^2+e+1)$
• D. All of these

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The total time taken in moving from $O$ to $C$ is $\frac{a}{e^{2}u}(e^2+e+1)$
B The free range on the horizontal plane $b=\frac{2uv}{g}$
C $b{e}^2=a(e^2+e+1)$
D All of these

$R=\frac{2u_x{u}_y}{g}=\frac{2uv}{g}=b$
$t=\frac{a}{u}+\frac{a}{eu}+\frac{a}{e^{2}u}=\frac{a}{u}(1+\frac{1}{e}+\frac{1}{e^2})$
$=\frac{a}{u}\left(\frac{e^2+e+1}{e^2}\right)=\frac{a}{e^{2}u}(e^2+e+1)$
$\therefore \frac{2v}{g}=\frac{a}{e^{2}u}(e^2+e+1)$
$\therefore b{e}^2=a(e^2+e+1)$