Jane, whose mass is 50kg, needs to swing across a river (having width d) filled

Question

Jane, whose mass is 50kg, needs to swing across a river (having width d) filled with man eating crocodiles to save Tarzan from danger. However, she must swing into a wind exerting with constant horizontal force F on a vine having length L and initially making an angle ? with the vertical. Taking d=50m, F=110N, L=40m, and ?=50degrees. a) With what minimum speed must Jane begin to swing to just make it to the other side? b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80kg. Jane, whose mass is 50kg, needs to swing across a river (having width d) filled with man eating crocodiles to save Tarzan from danger. However, she must swing into a wind exerting with constant horizontal force F on a vine having length L and initially making an angle ? with the vertical. Taking d=50m, F=110N, L=40m, and ?=50degrees. a) With what minimum speed must Jane begin to swing to just make it to the other side? b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80kg.

Explanation / Answer

Part a) D = Lsin? + Lsinf, 50=40(sin50+sinf), f = 28.9 degrees Ki + Ui + Wwind = Kf + Uf 1/2mvi2 + mg(-Lcos?) + FD(-1)=0+mg(-Lcosf) 1/2(50)(vi)2 + 50(9.8)(-40cos50)-110(50) = 50(9.8)(-40cos28.9)
vi = 6.15 m/s Part b) 1/2mvi2 + mg(-Lcosf) + FD(+1) = 0+mg(-Lcos?) 1/2(130)(vi)2 + 130(9.8)(-40cos28.9)+110(50) = 130(9.8)(-40cos50) vi = 9.87 m/s

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