An 94.5-kg mountain climber plans to swing down, starting from rest, from a ledg

Question

An 94.5-kg mountain climber plans to swing down, starting from rest, from a ledge using a light rope 8.55 m long. He holds one end of the rope, and the other end is tied higher up on a rock face. Since the ledge is not very far from the rock face, the rope makes a small angle with the vertical. At the lowest point of his swing, he plans to let go and drop a short distance to the ground.

(a) How long after he begins his swing will the climber first reach his lowest point?

(b) If he missed the first chance to drop off, how long after first beginning his swing will the climber reach his lowest point for the second time?

Explanation / Answer

Apply T = 2pi(sqrt(l/g))

T = 2pi(sqrt(8.55/9.8)

T = 5.86 sec

To get to the bottom, that is 1/4th of the period

5.86/4 = 1.47 sec

For the second chance, it is 3/4 of the period

.75(5.86) = 4.40 sec

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