Tarzan must save Jane from the Lion! But look out for those gaters below! Tarzan

Question

Tarzan must save Jane from the Lion! But look out for those gaters below! Tarzan grabs a Jungle vine attached to a tree limb. The Vine is 20 Meters long and attached to the tree limb just above Jane. Tarzan swings on the vine. Just as Tarzan reaches Jane he lets go of the vine and grabs tightly onto Jane. Tarzan and Jane fall clinging together into the water below. They are safe and swim to the nearby shore. Assume Tarzan and Jane can be treated as point masses located at their center of mass. The dimensions in the diagram are the locations of their center of mass. Tarzan's mass is 60 Kg and Jane's mass is 30 kg. Assume air resistance is negligible and that the vine is taut, flexible and mass less. L1 = 20 meters, L2 = 40 meters, J-T = 20 meter: (a) What is the speed of Tarzan just before the collision with Jane? (b) What is the tension in the vine just before the collision with the Jane? Note that Tarzan is experiencing circular motion. (c) After Tarzan hits and grabs Jane, What is the speed of their combined masses? (d) Determine the total horizontal displacement, X, of Tarzan from position "T" until Tarzan and Jane land in the water at point "Q".

Explanation / Answer

A) v = sqrt(2gh) = sqrt (2*9.8*20) = 19.8 m/s

B) T = mg + mv^2 /R= 60*9.8+60*392 /20= 1764 N

C) by momentum conservation in horizontal direction,

(30+60)v = 60*19.8

v = 13.2 m/s

D) time taken to fall = sqrt(2h/g) = sqrt (2*40/9.8) = 2.857s

X = 20+2.857*13.2

= 57.7 m answer

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