Work and Power Homework problem

[Santorican]

This question, I have absolutely no idea what to do.


Question: Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 m that makes an angle of 45 degrees with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of 30 degrees with the vertical.

Part A)
Calculate Tarzan's speed just before he reaches Jane. You can ignore air resistance and the mass of the vine.

I figured that I am going to have to use the work energy theorem, W=change in K and then break it down into smaller bits, but there is no mass and I have no idea what work is equal to so I am totally stumped.

 

[Redbelly98]

Try using conservation of energy. The vine does not actually do any work on Tarzan.

 

[Santorican]

So by using Ue=Uk and breaking it down I can figure out the answer!? That is so beautifully simply!

Thank you

 

[Santorican]

Okay so I tried using the conservation of energy Ue=Ke and then broke it down to mgh=(mv^2)/2 and then simplified to find velocity but this is where I am confused.

I tried using V=(2gh)^1/2 and it was wrong.

Then I tried to find the component of gravity at a 30 degree angle with respect to y and used V=(2(sin30g)h)^1/2 and it was wrong.

Then again with respect to x, don't have a clue at this point, V=(2g(cos30)h)^1/2 and it too was wrong.

So right now I am utterly completely lost. Please help :(

 

[Redbelly98]

Well, for conservation of energy you need 4 quantities to set up the equation:
initial kinetic energy and initial potential energy
final kinetic energy and final potential energy