A particle \(P\) of mass \(2 m\) is moving in a straight line with speed \(3 u\) on a smooth horizontal plane. It collides directly with a particle \(Q\) of mass \(m\) that is moving on the plane with speed \(2 u\) in the opposite direction to \(P\).
The coefficient of restitution between \(P\) and \(Q\) is \(e\), where \(e > \frac { 4 } { 5 }\)
Show that the speed of \(Q\) immediately after the collision is \(\frac { ( 4 + 10 e ) u } { 3 }\)
After the collision \(Q\) hits a smooth fixed vertical wall that is perpendicular to the direction of motion of \(Q\). The coefficient of restitution between \(Q\) and the wall is \(f\).
Find, in terms of \(\boldsymbol { e }\), the set of values of \(f\) for which there will be a second collision between \(P\) and \(Q\).