Momentum and CollisionHardBloom L3

Question

In a smooth stationary cart of length d, a small block is projected along it's length with velocity v towards front. Coefficient of restitution for each collision is e. The cart rests on a smooth ground and can move freely. The time taken by block to come to rest w.r.t. cart is

Options

A.$\frac{ed}{(1 - e)v}$
B.$\frac{ed}{(1 + e)v}$
C.$\frac{d}{e}$
D.infinite

Solution

Sol. Total time = $\frac{d}{v} + \frac{d}{ev} + \frac{d}{e^{2}v} + ......$

= $\frac{d}{v}\left( 1 + \frac{1}{e} + \frac{1}{e^{2}} + ..... \right)$

Since $\frac{1}{e} > 1$ ⇒ total time = infinite.

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