A tetherball apparatus consists of a ball attached to a 2.30 m rope that is atta

Question

A tetherball apparatus consists of a ball attached to a 2.30 m rope that is attached in turn to the top of a 2.70 m tall pole. The ball is struck such that it moves horizontally around the pole. Immediately after the ball is struck, it moves at 5.83 m/s, and experiences a centripetal acceleration of 1.74g (where g is the acceleration due to gravity of a falling object near Earth's surface). If the resulting path of the ball is approximately a circle, what is the height h of the ball above the ground?

Explanation / Answer

Let it rotate in a circle of radius r.

Given centripetal acceleration.

v^2/r = g

5.83^2/r = 1.74 * 9.8

r = 2 m

Height of the ball above the ground = 2.7 - sqrt(2.3^2 - 2^2) = 1.564 m

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