A body of mass m makes an elastic collision with another identical body at rest. Show that if the collision is not head-on, the bodies go at right angle to each other after the collision.

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Solution

According to the question, the collision of the two bodies of mass m is not head-on. Thus, the two bodies move in different directions.

Let the velocity vectors of the two bodies after collision be v₁ and v₂.

As the collision in the question is elastic, momentum is conserved.

On applying the law of conservation of momentum in X-direction, we get:

$m u_{1} + m \times 0 = m v_{1} \cos α + m v_{2} \cos β . . . (i)$

On applying the law of conservation of momentum in Y-direction, we get:

$0 = m v_{1} \sin α - m v_{2} \sin β . . . (i i)$

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