Some physics help?

Question

Jane, whose mass is 45.0 kg, needs to swing across a river filled with man-eating crocodiles in order to rescue Tarzan, whose mass is 80.0 kg. 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.) In the figure, D = 50.0 m, F = 118 N, L = 40 m, and theta = 50.0°.
http://www.webassign.net/sercp/p5-73.gif
(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?
m/s
Any help would probably be appreciated... ^^

Answer 1

When Jane jumps she will lose energy to the wind and lose PE
Her starting kinetic energy must be great enough to overcome these energy losses

To compute the loss due to wind it is simple
F*D
or 118*50

For PE, Jane's starting height is
h1=L*(1-Cos(th))

and ending height is
h2=L*(1-cos(asin((50-L*sin(th))/L)))

so PE is m*g*(h1-h2)

put it all together

.5*m*v^2=F*D-PE
=8.94 m/s

For the return trip the new mass is 125 kg, the F*D is in their favor, and they must gain PE
.5*m*v^2=PE-F*D
or
.5*125*v^2=125*9.81*(14.3-5)-118*50
v=9.38 m/s


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