Elastic Collision Homework: Tarzan & Jane Reach Max Height Together

[dlynch851]

Homework Statement

The 80kg Tarzan swings from a 3m vine that is horizontal when he starts. At the bottom of his arc, he picks up 60kg Jane in an ELASTIC collision. Find max height they reach together.

2. Relevant equation
Wgrav= mgy1-mgy2
Wel=.5k(xi^2-xf^2)

The Attempt at a Solution

I have no solution for this I searched and only found inelastic collisions which have momentum in their solutions. We have not learned momentum therefore I'm trying to figure out how all this pieces together with conservation of energy and corresponding variables.

Initially I found tarzan's Vf right before getting to Jane by using W= delta-KE. Once this was found I set up the equation for conservation of energy Ki+Pi = Kf+Pf. I used combined masses in this step.

Am I on the right path here also should I have used the radius(vine length) in there to calculate his velocity?

Thanks

 

[andrewkirk]

This question contains hidden presuppositions that may not be true - like the famous 'have you stopped beating your wife' question.
The presupposition is that the two bodies remain together after an elastic collision. I haven't done the calcs to check, but I doubt this is possible. Usually two bodies remain together only after inelastic collisions. If I'm correct then the situation is impossible.

What I think the question asker was trying to achieve was to turn it into a simple question about conservation of energy, and saying the collision is elastic allows one to focus exclusively on energy in this case.

If we ignore the suspected impossibility of the scenario and just ask to what height the pair would rise if such an energy-conserving event were possible, we can just equate total energy at the beginning and end of the arc to the kinetic energy and solve. If we label the start, bottom of arc and end as times 1, 2 and 3 then we have

PE3+KE3=PE2+KE2=PE1+KE1

You're only interested in PE3 and PE1, so you don't need to calculate KE2 - so no need to calculate velocity. You do need to use the vine length though, to get expressions for (PE3-PE2) and (PE1-PE2).

 

[haruspex]

If we ignore the suspected impossibility of the scenario and just ask to what height the pair would rise if such an energy-conserving event were possible

I cannot accept that resolution. If the consequence is that the answer violates momentum conservation then it is not an answer. If p is false then p implies q, whatever statement q is.

In fact, there is a way to make it elastic. Instead of (dangerously) hurtling straight into poor Jane, he aims to miss her by a couple of arm's lengths. At closest approach, they reach out sideways and smoothly clasp hands. End result is that momentum conservation determines the speed of their common mass centre, and all the excess KE goes into spinning them around each other.

But I would not surprised if the question statement has simply become garbled, and it should say inelastic.