A smooth sphere P of mass $\displaystyle 2m$ is moving in a straight line with speed $\displaystyle u$ on a smooth horizontal table. Another smooth sphere Q of mass $\displaystyle m$ is at rest on the table. The sphere P collides directly with Q. The coefficient of restitution between P and Q is $\displaystyle \frac{1}{3}$. The spheres are modelled as particles.

(a) Show that, immediately after the collision, the speeds of P and Q are $\displaystyle \frac{5}{9}u$ and $\displaystyle \frac{8}{9}u$ respectively.

After the collision, Q strikes a fixed vertical wall which is perpendicular to the direction of motion of P and Q. The coefficient of restitution between Q and the wall is e. When P and Q collide again, P is brought to rest.

(b) Find the value of e.

(c) Explain why there must be a third collision between P and Q.

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I've done part (a) by forming 2 simultaneous equations of conservation of momentum and Newton's law of restitution and solving to obtain the values required. For part (c), I know that collusion must occur as particle P is rebounded so it will hit the stationary particle Q.

The only aspect I don't understand is part (b). How would I do this?

Thanks in advance.