Momentum and work energy question

[nugget]

Homework Statement

Two kids on roller skates push off each other in opposite directions. One weighs 36kg and he rolls 15m before stopping, the other weighs 24kg, how far does he move before stopping? Assume they experience the same frictional force by the path - assume friction force is negligible during the time the push each other away - This involves both momentum and work energy.

Homework Equations

From the question I assume this involves conservation of momentum equations and a work-energy equation (but i don't know any!)

The Attempt at a Solution

I tried to use straight line motion equations but we are not given initial velocity, then I tried to use momentum equations but couldn't and am now at a loss.

 

[Delphi51]

Yes, a peculiar question.
Conservation of momentum applies to the pushing apart. They begin with zero momentum, so they still have zero momentum after pushing apart. The mv for one will be minus the mv of the other. Each has momentum p = mv.

During the stopping, they do work on the ice through the friction force. This dissipates the kinetic energy. So you must now think in terms of kinetic energy, not momentum.
K = .5*m*v^2 = p^2/(2m)
The idea is to keep the p (forget the v) because you know p is the same for both skaters.

To finish it, do K = W = F*d for the skater with the known stopping distance.
This should give you an expression for the friction force F.

Then do K = F*d for the second skater and replace F with that expression.
Finally, solve for d and calculate.

 

[nugget]

hey i get 22.5, have i done it correctly?

 

[Delphi51]

Right on!