Jane, whose mass is 46.5 kg, needs to swing across a river (having width D) fill

Question

Jane, whose mass is 46.5 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 ? with the vertical (see below figure). Take D = 51.0 m,
F = 105 N,L = 40.0 m, and ? = 45.0°

A-With what minimum speed must Jane begin her swing to just make it to the other side

B-Once the rescue is complete, Tarzan and Jane must swing back together across the river. With what minimum speed must they begin their swing? Assume that Tarzan has a mass of 77.6 kg

Explanation / Answer

Part a) D = Lsin? + Lsinf, 51=40(sin45+sinf), f = 34.6 degrees Ki + Ui + Wwind = Kf + Uf 1/2mvi2 + mg(-Lcos?) + FD(-1)=0+mg(-Lcosf) 1/2(46.5)(vi)2 + 46.5(9.8)(-40cos45)-105(51) = 46.5(9.8)(-40cos34.6) vi = 11.8 m/s Part b) 1/2mvi2 + mg(-Lcosf) + FD(+1) = 0+mg(-Lcos?) 1/2(124.1)(vi)2 + 124.1(9.8)(-40cos34.6)+105(51) = 124.1(9.8)(-40cos45) vi = 2.16 m/s

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