Physics?

cc: Physics?
tarzan and jane, whose total mass is 130.0 kg, start their swing on a 5.0 m long vine when the vine is at an angle of 30 degrees with horizontal. At the bottom of the arc, Jane, whose mass is 50.0 kg,releases the vine. What is the maximum height at which tarzan can land on a branch after his swing continues

Answers and Views:

Answer by Andrew A
The technically correct answer would be slightly lower than the height as when he started. If Jane simply releases the vine she will carry on moving horizontally and so take all of her energy with her. Since all systems are lossy he could never get back to the same height as which he started.

However I’m guessing that isn’t the answer they want so instead I’ll make the stupidly unrealistic assumption that Jane somehow releases the vine in such a way that she has no horizontal velocity. I’ll also assume that this is a lossless system.
That then turns this into a conservation of energy question.

A 5m vine which is 30 degrees from horizontal.
Taking the origin as being the point where the vine is hanging from his initial altitude is -5*sin(30) = -2.5m
At the bottom of the swing his altitude is -5*sin(90) = -5m

Total kinetic energy at the base of the swing = potential energy lost = 2.5*g*130.

All of that energy is then converted into potential energy as Tarzan goes back up into the air.
So his potential energy at the end is h*g*(130-50)
Conservation of energy means that
h*g*(130-50) = 2.5*g*130
h = 2.5*130 / 80 = 4.06

Se he ends up about 4 meters from the low point of the swing or 1.5m higher than he started.