A ball of mass m moving horizontally at a speed v collides with the bob of a simple pendulum at rest. The mass of the bob is also m. If the collision is perfectly elastic, the bob of the pendulum will rise to a height of

In an elastic collision between two bodies of the same mass with one of them initially at rest, the moving body is brought to rest and the other moves with the same speed. Thus the ball will come to rest and the bob of the pendulum acquires a speed v. At this speed, it will rise to height h given by $h = v^2 /2g$.