Solve Momentum Problem: Ice Skater & Cube

[fightboy]

Homework Statement

A large, uniform-density cube of styrofoam has a side length of 3.0 m and a mass of 90 kg. It is at
rest on a horizontal, frictionless (ice) surface. An ice-skater with a mass of 60 kg is standing at rest,
touching one face of the cube. You should consider all of the ice-skater's mass to be located exactly at
the position of the cube's side. The ice-skater now pushes off against the cube. When the cube has
moved 4.0 m from its starting position, how far has the ice-skater moved?

Homework Equations

mv_i=mv_f,
hard to tell what other equations come into play[/B]

The Attempt at a Solution

tried to use conservation of momentum equation (mv_i=mv_f) to solve, but ended up falling short since I can't determine the velocities of the cube and the ice-skater. I know information about the side length of the cube and the ice skater's position on the cube will be important in figuring out the problem, but i just can't see how they are connected.

 

[Simon Bridge]

The conservation of momentum equation will give you one equation with two unknowns - you need to find another equation (or two) in those unknowns.

You have yet to use the distances - what is the relationship between the distance traveled and the velocity?

Note: you can also do this in terms of ratios - what is the skaters speed as a fraction of the cube's?
What does that suggest about the distances they travel in the same time?

 

[CWatters]

I tried to use conservation of momentum equation (mvi=mvf) to solve, but ended up falling short since I can't determine the velocities of the cube and the ice-skater.

What Simon said.

Write your equations.
Substitute Velocity = distance/time

You might find that the time cancels :-)