A smooth sphere P of mass is moving in a straight line with speed on a smooth horizontal table. Another smooth sphere Q of mass is at rest on the table. The sphere P collides directly with Q. The coefficient of restitution between P and Q is . The spheres are modelled as particles.
(a) Show that, immediately after the collision, the speeds of P and Q are and 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.
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.