Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a collision with no outside force, momentum is conserved: . In an elastic collision kinetic energy is conserved too. Head-on and elastic, with the target at rest: , .
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. , .
Step 1. (a) Equal masses. and : they swap velocities.
Step 2. Light hits heavy. and : the light ball bounces straight back, like a ball off a wall.
Step 3. Heavy hits light. and : the heavy ball barely slows, and the light one flies off at twice its speed.
Answer: (a) The first stops; the second moves at . (b) Light on heavy: it bounces back. Heavy on light: the light one leaves at about .
Watch out. These shortcuts hold only for elastic, head-on collisions with the target at rest.
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