Help Solve Energy Problem 2: Tarzan & Jane's Swing

[Port]

i kinda also need help on another problem. i can't even start this problem because i have no idea how! can someone please tell me how?

Tarzan and Jane, whose total mass is 130kg, start their swing on a 5m long vine when the vine is at an angle of 30 degrees with the horizontal. At the bottom of the arc, Jane, whose mass is 50kg, releases the vine . What is the max height at which Tarzan can land on a branch after his swing continues?

 

[Yapper]

ok so its 30 degrees from the horizanrtal and the rope is 5m long so you can fidn the diference from their current height and the height at the bottom of the arc right? with that height you can use the potential energy formula mgh(mass x gravity x height). And I think, not totally sure, you can set that equal to the potential energy at the max height reached which would be mass of just tarzan x gravity x max height. solve for max height

 

[HallsofIvy]

In order to be able to do this, you need to assume some initial speed- probably you are to assume that Tarzan and Jane just grab the vine and drop so the initial speed is 0. You know the initial height compared to the height at the bottom of the arc- it's
r- r cos(θ)= r(1- cos(30))= $r\frac{2-\sqrt{3}}{2}$- so you can calculate the change in potential energy= kinetic energy and so the velocity at the bottom of the arc. Tarzan now has that velocity so you can calculate his kinetic energy and convert that to potential energy to find the maximum height.

HOWEVER, I believe that the two persons could be treated separately anyway- I can see no reason why Tarzan would not rise up to the same height as initially.