Conservation of Energy

Question

In order for Jane to return to base camp, she needs to swing across a river of width D that is filled with alligators. She must swing into a wind exerting constant horizontal force F,

 on a vine having length L and initially making an angle 𝜃 with the vertical (see below figure). Take D = 50.0 m,

 F = 113 N,

 L = 40.0 m,

 𝜃 = 47.0°,

 and her mass to be 50.0 kg.

(a)With what minimum speed (in m/s) must Jane begin her swing to just make it to the other side? (If Jane can make it across with zero initial velocity, enter 0.)

(b)Shortly after Jane's arrival, Tarzan and Jane decide to swing back across the river (simultaneously). With what minimum speed (in m/s) must they begin their swing? Assume that Tarzan has a mass of 80.0 kg.

Answer 1

With no picture, there's a little bit of guessing on my end as to what it shows, in particular regarding the starting and ending heights of the swing. However, the idea is that if we were to disregard the wind, and friction of the vine, no energy would be lost and when Jane got to the same height on the way up, she would be moving at the same speed. However, the wind does negative work, and we need to set up an integral to determine the amount of work done by the wind, in terms of theta. Figuring out this amount of work, will determine the amount of extra kinetic energy we need at the start to get across.

Answer 2

Using Work- Kinetic Enegy Theorem: F x D = 1/2 m v²; solve for v : v²= 2FD/m so v = sq rt of 2FD/m

Jane’s velocity 10.7 m/s

Tarzan & Jane’s velocity 6.65 m/s