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**1. Homework Statement**

A verbatim copy from the problem set:

Two children wearing skates on ice push apart from each other in opposite directions. The child of mass 30kg slides 15m before stopping. How far will the smaller child of mass 20kg travel before stopping? Assume they experience the same frictional force by the ice. However, the frictional force is negligible during the time they push each other away. (This question involves energy and momentum).

**2. Homework Equations**

The "This question involves energy and momentum" through me off a bit because I was originally looking at just momentum. I suppose that the equations involved are:

[tex]\sum[/tex]P(initial) = [tex]\sum[/tex]P(final)

E(kinetic) = [tex]\frac{1}{2}[/tex]mv[tex]^{2}[/tex]

[tex]\sum[/tex]F = [tex]\frac{dP}{dt}[/tex] = m[tex]\frac{dv}{dt}[/tex]

**3. The Attempt at a Solution**

The absense of any time makes the above equation with dt in it a bit hard.

Is the acceleration constant (slowing each skater down)? I would have thought so because the kinetic friction force is generally constant.

I've drawn out the basic situation in my book but this addition of energy to the problem is confusing me. We've only had a small talk about energy so far in the lectures so all I have to go on is my memory of first semester of last years high school physics which is now a fair time ago.

What would be the recommended starting point? I was thinking that looking at the initial vs final momentum (both being zero) wouldn't be of much use as neither of them take into account the displacement. I know that this all sounds like a pretty poor attempt at the solution but I really am baffled and it has come as the hardest of the 6 questions on the problem set to other people I've talked to (it is question 6).