Jane, whose mass is 45.0 kg, needs to swing across a river (having width D) fill

Question

Jane, whose mass is 45.0 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 ? with the vertical (see below figure). Take D = 51.0 m, F = 119 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? (If Jane can make it across with zero initial velocity, enter 0.)

_________m/s

(b) Once the resue is complete, Tarzan an Jane must swing back together across the river. with what minimum speed must they begin their swing? Assume Tarzan has a mass of 87.2 kg.

_________m/s

Explanation / Answer

  Given m=45.0kg, D=51.0m, F=119N, L=40.0m, 1=45.0°, g=9.81m/s
(a)The final angle 2 can be found from the horizontal distance:
D = Lsin1+Lsin2
Solving for 2 gives us:
2 = asin((D/L)-sin1) = 34.6

The initial & final heights are given by:
h1 = L(1-cos1) = 11.715 m
h2 = L(1-cos2) = 7.075m

By conservation of energy, initial height & speed into wind become final height:
mgh1+½mv²-FD = mgh2
Solving for v gives us:
v = (2g(h2-h1)+(2FD/m)) = 13.37 m/s

(b)Given m=132.2kg, Assume 1=45°
As above: 2= 34.6 °, h1=11.7m, h2= 7.075m

By conservation of energy, initial height & speed with wind become final height:
mgh1+½mv²+FD = mgh2
Solving for v gives us:
v = (2g(h2-h1)-(2FD/m)) = not possible with given data

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