# Conservation of momentum problem in variable.

1. Oct 7, 2009

### CandyApples

1. The problem statement, all variables and given/known data
Tarzan mass M swings from a vine from rest at height H. At the bottom of the arc he picks up Jane of mass m in a perfectly inelastic collision. They reach a vertical height h. How far vertically above h is H?

2. Relevant equations
Pi = Pf
R = $$\Sigma$$mr/$$\Sigma$$m

3. The attempt at a solution
Using conservation of momentum:
Mv1 = (M + m)v2
Center of mass:
(MH + (m+M)h)/(m + M)

I feel as though these must somehow be related to find the distance, but after looking for quite some time now, no obvious correlations are coming. I would appreciate any help in getting me in the right direction. Thanks!

2. Oct 7, 2009

### rock.freak667

So we can find v2 in terms of v1.

Can you find v1 in terms of H ? (think energy)

At the bottom of the arc, Tarzan has 0 potential energy and only kinetic energy. This kinetic energy is converted into gravitational potential energy to the height h.

Can you find a relation between h and H now?

3. Oct 7, 2009

### CandyApples

Yes it is now much easier, thank you so much.