A ball is projected from a point near the bottom of one of the two parallel smooth vertical walls towards the other in a plane perpendicular to both walls. After two collisions at A & B it lands near the bottom of the other wall. Separation between the walls is ‘a’ and e is the coefficient of restitution for each collision. ( $\int \sec θ d θ = \ln (\sec θ + \tan θ) + C$ )

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Total time taken to move from O to C is $\frac{2 u_{y}}{g}$

Horizontal range of the ball in absence of the walls will be $a (1 + e + e^{2})$

Total time taken to move from O to C is $\frac{a}{e^{2} u_{x}} (1 + e + e^{2})$

Horizontal range of the ball in absence of the walls will be $a (1 + \frac{1}{e} + \frac{1}{e^{2}})$

answer is A, B, C.

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Detailed Solution

During collision with smooth wall velocity component parallel to wal does not change.

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