Hi! Tarzan and Jane, whose total mass is 130 kg, start their swing on a 5.0 m lo

Question

Hi!
Tarzan and Jane, whose total mass is 130 kg, start their swing on a 5.0 m 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 50 kg, steps off. What is the maximum height at which Tarzan can land on a branch after his swing continues?
Okay, the intial height (now) makes sense.
h sin theta or (5m) sin 30 = 2.5m
KE + PE = KE + PE or 0 + mg(2.5) = 1/2 mv^2 + 0
mass cancesl and v^2 = 2g(2.5) is v = 7 m/s
Tarzan swings up is
?1/2 m(2g)2.5m +0 = 0 + mgh ?
PE + KE = KE + PE
I found the answer in multiple places, it's 2.5 m in height. But HOW? And why find the velocity if it isn't needed? Thank you!

Explanation / Answer

P.E. = m1gh + m2gh = 50x 9.81x2.5 + 80x 9.81 x 2.5 = 3188.25 N-m K.E. = 3188.25 = 0.5 x 130 x v^2 v^2 = 49.05 v = 7.003 m/s with this velocity tarzan alone proceed further K.E. = 0.5 x 80 x 49.05 = 1962 N-m P.E. = 1962 = 80 x 9.81 x h h = 2.5 m ans

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