Jane, whose mass is 45.0 kg, needs to swing across a river filled with man-eatin

Question

Jane, whose mass is45.0kg, 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).D= 50.0 m,F=122N,L= 40 m, and?= 50.0.

Jane, whose mass is45.0kg, 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).D= 50.0 m,F=122N,L= 40 m, and?= 50.0. (a) With what minimum speed must Jane begin her swing in order to just make it to the other side? (Hint: First determine the potential energy that can be associated with the wind force. Because the wind force is constant, use an analogy with the constant gravitational force.) ____m/s (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 that Tarzan has a mass of 80.0 kg. ____m/s

Explanation / Answer

Given m=50.0kg, D=50.0m, F=122N, L=40.0m, ?1=50.0°, g=9.81m/s (a)The final angle ?2 can be found from the horizontal distance: D = Lsin?1+Lsin?2 Solving for ?2 gives us: ?2 = arcsin((D/L)-sin?1) = 28.94° The initial & final heights are given by: h1 = L(1-cos?1) = 14.28m h2 = L(1-cos?2) =4.994m By conservation of energy, initial height & speed into wind become final height: mgh1+½mv²-FD = mgh2 Solving for v gives us: v = v(2g(h2-h1)+(2FD/m)) = 7.87m/s (b)Given m=125.0kg, Assume ?1=50° As above: ?2=28.94°, h1=14.28m, h2=4.994m By conservation of energy, initial height & speed with wind become final height: mgh1+½mv²+FD = mgh2 Solving for v gives us: v = v(2g(h2-h1)-(2FD/m)) = m/s

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