A ball of mass m makes an elastic collision with another identical ball at rest. Show that if the collision is oblique, the bodies go at right angles to each other after collision.

Explanation

In head on elastic collision between two particles, they exchange their velocities. In this case, the component of ball 1 along common normal direction, v cos `theta` becomes zero after collision, while

that of 2 becomes v cos `theta`. While the components along common tangent direction of both the particles remain unchanged. Thus, the components along common tangent and common normal direction of both the balls in tabular form are given a head :

From the above table and figure, we see that both the balls move at right angles after collision with velocities v sin `theta` and v cos `theta`.