Jane wants to swing on a rope across a river. What minimum speed does she need to make it across, and once she's across, what minimum speed does she need to make it back? 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?