Tetherball

Consider a ball hung from rope of length \(l=2~\text{m}\) which is attached to the top of a vertical pole. Initially, the rope is vertical and the ball is given a horizontal initial speed \(v_{0}\). What is minimum initial speed \(v_{0}\) in meters per second for which the ball hits the top of the pole. Ignore friction, the mass of the rope and treat the ball as a point mass.

Details and assumptions

\(g=9.8~\text{m}/\text{s}^2\)

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