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A small ball is projected with a veloci...

A small ball is projected with a velocity u at some angle with horizontal towards a smooth vertical wall at a distance d from the point of projection after rebounding from the wall . If e is the coefficient of restitution then find maximum distance d for which ball may return to point of projection .

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To solve the problem of finding the maximum distance \( d \) for which a ball projected at an angle returns to the point of projection after rebounding from a smooth vertical wall, we can follow these steps: ### Step 1: Understand the motion of the ball The ball is projected with an initial velocity \( u \) at an angle \( \theta \) to the horizontal. It will travel towards the wall and rebound off it. The motion can be analyzed in two components: horizontal and vertical. ### Step 2: Calculate the time to reach the wall The horizontal component of the velocity is given by: \[ ...
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