7. Three particles \(P , Q\) and \(R\) lie at rest in a straight line on a smooth horizontal table with \(Q\) between \(P\) and \(R\). The particles \(P , Q\) and \(R\) have masses \(2 m , 3 m\) and \(4 m\) respectively. Particle \(P\) is projected towards \(Q\) with speed \(u\) and collides directly with it. The coefficient of restitution between each pair of particles is \(e\).

1. Show that the speed of \(Q\) immediately after the collision with \(P\) is \(\frac { 2 } { 5 } ( 1 + e ) u\). After the collision between \(P\) and \(Q\) there is a direct collision between \(Q\) and \(R\).
   Given that \(e = \frac { 3 } { 4 }\), find
2. 1. the speed of \(Q\) after this collision,
   2. the speed of \(R\) after this collision. Immediately after the collision between \(Q\) and \(R\), the rate of increase of the distance between \(P\) and \(R\) is \(V\).
3. Find \(V\) in terms of \(u\).