7. Three particles \(P , Q\) and \(R\) lie at rest in a straight line on a smooth horizontal surface with \(Q\) between \(P\) and \(R\). Particle \(P\) has mass \(m\), particle \(Q\) has mass \(2 m\) and particle \(R\) has mass \(3 m\). The coefficient of restitution between each pair of particles is \(e\). Particle \(P\) is projected towards \(Q\) with speed \(3 u\) and collides directly with \(Q\).

1. Find, in terms of \(u\) and \(e\),
   1. the speed of \(Q\) immediately after the collision,
   2. the speed of \(P\) immediately after the collision.
2. Find the range of values of \(e\) for which the direction of motion of \(P\) is reversed as a result of the collision with \(Q\). Immediately after the collision between \(P\) and \(Q\), particle \(R\) is projected towards \(Q\) with speed \(u\) so that \(R\) and \(Q\) collide directly. Given that \(e = \frac { 2 } { 3 }\)
3. show that there will be a second collision between \(P\) and \(Q\).