Jane, whose mass is 50 kg, needs to swing across a river having width D (50 m). She must swing into a wind with force F = 100 N while on a vine of length L (40 m) and initially making an angle theta of 50 degrees with the vertical. What minimum speed must Jane have to just make it to the other side?
m = 50kg, θ = 50, L = 40m, D = 50m, F = 110N.
PE = mgh, KE = 1/2*m*v^2, W = F*d, p = m*v(?)
The Attempt at a Solution
Jane's energy has to be greater than that of the wind in order to get across the gap. So I found W_wind = 110N * 50m and subtracted that from Jane's potential energy. I found her height using h = L (1 - cosθ) = 14.29m. I then subtracted the wind's energy from that and deduced that the left over energy is from KE so I solved for v using KE = 1/2mv^2. The problem is, I don't think I did this right. This is in a chapter called linear momentum and collisions and I didn't use either in this problem. I'm studying for a test tomorrow and there's a good chance something like this will be on it. Was this even the right approach?