Solving Jane's Swing Problem: Find Min Speed to Cross River & Return

[kreil]

This is the question I have from my book, I have tried numerous methods of solving it, but I cannot obtain the correct answers. If someone could get me started with an equation I could go from there...

Jane, whose mass is 50kg, needs to swing across a river (having width D) filled with man eating crocodiles to save Tarzan from danger. She must swing into a wind exerting a force F, on a vine having length L and initially making an angle theta with the vertical.

Taking D=50m, F=110N, L=40m and Theta=50 degrees...

a)with what minimum speed must Jane begin her swing in order to just make it to the other side?

b)Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80kg.


Well for part a I figured that since she is JUST going to make to the other side..

$$E_{Jane}-W_{wind}=0$$

$$\implies mg \Delta h+\frac{1}{2}mv^2-F_{wind}d=0$$

or

$$mg \Delta h + \frac{1}{2}mv^2=F_{wind}d$$

This expression seems like what I want, the only problem is that I can't find delta h..

Part (b) is obviously closely related to (a), so I just want to do a first.



Thanks
Josh

 

[whozum]

You need to show some work. Read the guidelines you agreed to.

 

[kreil]

work posted

 

[whozum]

Define angle alpha to be the angle swept by the rope from its point of fixation (at the top of the tree or whatever), When Jane is hanging directly down she will be L meters away from the top, when she is about to swing (with the 50 deg angle), she is L meters away from the top at a 50 deg angle from the vertical, there's a trig function that will show you her displacement in the Y direction.. remember the rope is the hypotenuse here.