Momentum and CollisionHardBloom L3

Question

In a one–dimensional collision between two particles, their relative velocity is ${\overrightarrow{v}}_{1}$ before the collision and ${\overrightarrow{v}}_{2}$ after the collision

Options

A.${\overrightarrow{v}}_{1} = {\overrightarrow{v}}_{2}$ if the collision is elastic
B.${\overrightarrow{v}}_{1} = - {\overrightarrow{v}}_{2}$ if the collision is elastic
C.$|{\overrightarrow{v}}_{2}| = |{\overrightarrow{v}}_{1}|$ in all cases
D.${\overrightarrow{v}}_{1} = - k{\overrightarrow{v}}_{2}$ in all cases, where k ≥ 1

Solution

Sol. $e = - \frac{\overrightarrow{v_{2}}}{\overrightarrow{v_{1}}}$

$\overrightarrow{v_{2}} = - e\overrightarrow{v_{1}}$

⇒ $\overrightarrow{v_{1}} = \left( \frac{- 1}{e} \right)\overrightarrow{v_{2}}$

$\because$ e ≤ 1

⇒ $\frac{1}{e}$ ≥ 1

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