Tarzan spies a chimpanzee of mass M in severe danger, so he swings to the rescue

Question

Tarzan spies a chimpanzee of mass M in severe danger, so he swings to the rescue. He adjust his strong, but very light vine so that he will first come rest at T seconds after beginning his swing, at which time his vine makes a {theta} angle with the vertical. Assume gravitational acceleration is g, and the vine is massless.

A/ how long is the vine, assuming Tarzan swings at the bottom end of the vine? I got as (T^2 * g)/(Pi)^2

B/What are frequency and Amplitude (in angle) of Tarzan's swing?

C/ Just as he passes through the lowest point in his swing, Tarzan nabs the chimp from the ground and sweeps him out of the jaws of danger. If Tarzan's mass is m, find amplitude of the swing with Tarzan holding the chimp. Would frequency change?

D/ What is conserved before & after grabbing the chimp? Will angular frequency change? Is linear momentum, angular momentum, total energy or kinetic energy conserved?

Thanks for the help

Explanation / Answer

part a )

time period of tarzan like simple pendulam = T = 2pisqrt(L/g)

here T = 2T

L = T^2*g/pi^2

part b ) frequncy = 1/T = 1/2T

part c )

E = Umax = mgh = mgL(1-costheta)

theta = cos^-1( 1 - E/mgL)

part d )

there is inelasitic collison

linear momentum remain conserve

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