Linear momentum and energy problem

[cero39]

Homework Statement

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.

Homework Equations

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?

 

[vela]

At what height does she end up at when she gets across the river? Your attempt assumes that she reaches the other side at the bottom of the swing.

 

[cero39]

Hm... It doesn't say but in the picture there is an angle phi to the left of the vertical, on the other side of theta. So she does swing past the vertical but no information is given as to how far past or how high...

 

[vela]

You have to calculate where she ends up. You know she travels 50 meters horizontally, and you can calculate how far she travels horizontally as a function of theta, phi, and the length of the vine.

 

[cero39]

Right so once I find the height I calculate the energy needed to go that high (m*g*h_2), add it to that of the wind(F*d), subtract from the potential energy at the first height (7002.1 J), and use that as my KE?
If so, I get 6.16 m/s as my answer.

 

[vela]

Sounds good.

 

[cero39]

Great. Thank you.