Jane needs to swing across a river filled with man-eating crocodiles in order to

Question

Jane needs to swing across a river filled with man-eating crocodiles in order to rescue Tarzan from danger. However, she must swing into a constant horizontal wind force, F on a vine that is initially at an angle of with the vertical see Fig. P5.73 Use these values to solve the problem anes mass 4 0 . Tarzan's mass 80 . D 50 m,F=128 N, L = 40 m, and = 49.5 L. Wind Jane Tarzan Figure P5.73 (a) what is the angle , the final angle the vine makes with the vertical? 29.314 With what minimum speed must Jane begin her swing in order to just make it to the other side? If she can make it to the other side with zero initial speed, what is her final speed (enter this value with a negative sign)? 9.316 (b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? If they can make it to the other side with zero initial speed, what is their final speed (enter this value with a negative sign)? m/s m/s

Explanation / Answer

c) 1=49.5,L=40m,D=50m

D = Lsin1+Lsin2

2 = asin((D/L)-sin1) = 29.3

Given m=129.0kg, Assume 1=49.5°
As above: 2=29.3°h1 = L(1-cos1) = 14.4m
h2 = L(1-cos2) = 5.2m

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)) = 16.7m/s

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