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Here's what's given:

mass = 47 kg

horizontal wind - call it F - (opposite to her swing) = 120 N

horizontal distance (D) = 50 m

rope length (L) = 40 m

theta = 50 degrees

(hopefully you can see the image)

Here's how I started:

D = Lsin(theta) + Lsin(phi)

Plug in the values, and phi = 28.9 degrees

Then, Change in height = Lcos(phi) - Lcos(theta)

Plug in the values, change in height = 9.3 m

From there:

PE(o) + KE(o) + wind = PE(f) + KE(f)

mgh(0) + (1/2)mv(0)^2 - F(w)*D = mgh(f) + (1/2)mv(f)^2

and v(0) = 8.55 m/s

I got that part right. But, now how do I find the minimum velocity to go back? I tried switching the h(0) and h(f) in that last equation to go back, but it didn't work. What's wrong?