An 89.0-kg mountain climber plans to swing down, starting from rest, from a ledg

Question

An 89.0-kg mountain climber plans to swing down, starting from rest, from a ledge using a light rope 5.55 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?
s

(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?
s

Explanation / Answer

time period for swing T = 2pi sqrt(L/g) = 2pi sqrt(5.55 /9.81) =4.73 sec

A time period is time taken to come back to its starting point again.

time taken to reach at lowest point = T/4 = 1.18 sec

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b) again he will comes to lowest point after = 3T/4 =3.54 sec

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