Ball in cup

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In this demonstration, a ball is perched on the end of a thin board that is hinged at its opposite end and propped up in the air by a stick. Mounted on the thin board a short distance away from the ball is a cup. When the stick is jerked out from beneath the board and the board falls, will the ball end up in the cup?

The diagram below shows the trajectories for the ball and the cup. It is clear the cup has to travel farther than the ball (and faster) in order to end underneath the ball (so the ball can land in the cup). For the acceleration of the cup to be greater than the ball, there must be more force on the board than on the ball when it is in free-fall.

When the stick is jerked and the board falls, the ball is in "free-fall" due to gravity. The only force on the ball is its weight due to gravity. As the board/cup is falling, it too has the weight of gravity. However, since it is hinged at its lower end, there is a torque on the stick that causes the rotation of the stick. This torque is enough to get the ball under the cup as shown in the movie.

1. Identify the force couple on the board by using Newton's third law.
2. Using conservation of energy calculate the velocity of the ball as it hits the ground.
3. Using conservation of energy calculate the velocity of the end of the board as it hits the ground.