Tarzan and Jane inelastic collision?

Question

Tarzan, whose mass is 95.0 kg, swings from a 3.10 m vine that is horizontal when he starts. At the bottom of his arc, he picks up 60.0 Jane in a perfectly inelastic collision. What is the height of the highest tree limb they can reach on their upward swing?

I believe I need to use both inelastic collision equation
m1v1i +m2v2i = (m1 + m2)vf
as well as conservation of energy
KEi + PEi = KEf + PEf
(1/2)mvi^2 + mghi = (1/2)mvf^2 mghf
My problem is that I'm not sure how to use the inelastic collision equation because if I assume Tarzan starts at rest then the left side is equal to 0 but if I assume he has an initial velocity then I wind up with two unknowns, v1i and vf.

Answer 1

Actually with inelastic collision, conservation of energy does not apply.

So with conservation of momentum...
PE = KE which gives you v1i = 7.8 m/s = sqrt (3.1m * g * 2)
vf = 4.7775 m/s

PE = KE = 0.5 (155 kg) * (4.7775)^2 = 155kg * g * Height
Final height = 1.1645 m