Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) fill

Question

Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F, on a vine having length L and initially making an angle theta with the vertical (see below figure). Take D = 47.0 m, F = 106 N, L = 40.0 m, and theta = 50.0 degree. With what minimum speed must Jane begin her swing to just make it to the other side? (If Jane can make it across with zero initial velocity, enter 0.) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume that Tarzan has a mass of 80.0 kg.

Explanation / Answer

D = L(sin(theta) + sin(phi))

=> phi = arcsin(47/40 - sin(50)) = 24.13 degree

Apply energy conservation

=> 0.5*50*v^2 + 50*9.81*l(cos(phi) - cos(theta)) = 106*47

=> 25v^2 = 4982 - 50*9.81*40*(cos(50) - cos(24.13)) = -312.11

So initial speed = 0 Answer

For going back apply energy conservation and total mass = 50+80 = 130kg

=> 0.5*130*v^2 = 130*9.81*40*(cos(24.13) - cos(50)) - 106*47 = 8782.7

=> v = 11.62 m/s Answer

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