A small ball is projected horizontally between two large blocks. The ball is given a velocity Vm/s and the large blocks move uniformly with a velocity of 2Vm/s. The ball collides elastically with the blocks. If the velocity of the blocks do not change due to the collision, then find out the velocity of the ball after the 2nd collision. Assume friction to be absent.

Engineering

Physics

Newtons Second Law of Motion

Collision

Relative Motion

Question

A small ball is projected horizontally between two large blocks. The ball is given a velocity Vm/s and the large blocks move uniformly with a velocity of 2Vm/s. The ball collides elastically with the blocks. If the velocity of the blocks do not change due to the collision, then find out the velocity of the ball after the 2^nd collision. Assume friction to be absent.

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In elastic collisions where the block's velocity remains unchanged (infinite mass), the ball's velocity relative to the block reverses direction. Let the initial ball velocity be $V$ horizontally. Both blocks move at $2 V$ to the right.

Before first collision, relative velocity to right block is $V - 2 V = - V$ . After elastic collision, relative velocity becomes $+ V$ , so ball's new velocity is $2 V + V = 3 V$ right.

Before second collision with left block (moving right at $2 V$ ), relative velocity is $3 V - 2 V = V$ right. After collision, relative velocity reverses to $- V$ , so ball's final velocity is $2 V - V = V$ right.

Final answer: $V$ m/s to the right.