Question

If a 50 kg circus actor swings on a 25 m rope to reach a basketball 5 meters away which has a mass of 10kg. How long does it take for the actor to swing to the ball, collect it, and return to his initial position? then assume, that the actor starts at 5 meters, and at every peak of his swing he moves down 5 meters. How long does it take for him to reach the bottom of the rope.

Answer 1

Simple pendulum problem

we know that the time period of a simple pendulum is  

T = 2pi sqrt(L/g)

given L = 25 m , and g = 9.8 m/s2

we observed that there is no mass term in the formular of timeperiod so

here there is no significance of mass of circus actor and mass of basket ball

and time period by definition is time taken to complete one rotation which means , time for , to reach from one of the extream end to the mean position to other end again from other end to mean positon to the original position.

substituting the values  

Time period is T = 2pi sqrt(25/9.8)s

T = 10.03545 s

now the time taken for him to reach the bottom of the rope is one fourth of the time period

that is T' = T/4 = 10.03545/4 s = 2.50886 s

Answers

T = 10.03545 s

T' = 2.50886 s