Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A girl and a boy stand at rest on smooth ice and push each other away. The girl moves off at .
Only external forces move the centre of mass: . With no external force, the total momentum is conserved, and the centre of mass stays at rest or moves steadily.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Momentum, then distances.
Step 1. (a) , so , the other way.
Step 2. (b) In : and , so apart.
Step 3. (c) Still where they started: no external horizontal force acts.
Answer: (a) . (b) . (c) At the starting point.
Check. and : their moments about the start balance.
Watch out. The pushes are equal and opposite, but the lighter skater moves faster.
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