Question

$AB$ is an L−shaped obstacle fixed on a horizontal smooth table. A ball strikes it at $A$, gets deflected and restrikes it at $B$. If the velocity vector before collision is $\overrightarrow{v}$ and coefficient of restitution of each collision is $e$, then the velocity of ball after its second collision at $B$ is

Diagram

• A. $-e^2\overrightarrow{v}$
• B. $e^2\overrightarrow{v}$
• C. data insufficient
• D. $-e\overrightarrow{v}$

Answer 1

The correct option is D $-e\overrightarrow{v}$

During 1st collision perpendicular component of $v$, $v_{\perp }$becomes $e$ times, while $I{I}^{nd}$ component $v_{II}$\) remains unchanged and similarly for second collision.

The end result is that both $v_{\perp }$and $v_{II}$ become $e$ times their initial value and hence $V”=–eV$ (the ( – ) sign indicates the reversal of direction)

Diagram