6. Three identical particles, \(A , B\) and \(C\), lie at rest in a straight line on a smooth horizontal table with \(B\) between \(A\) and \(C\). The mass of each particle is \(m\). Particle \(A\) is projected towards \(B\) with speed \(u\) and collides directly with \(B\). The coefficient of restitution between each pair of particles is \(\frac { 2 } { 3 }\).

1. Find, in terms of \(u\),
   1. the speed of \(A\) after this collision,
   2. the speed of \(B\) after this collision.
2. Show that the kinetic energy lost in this collision is \(\frac { 5 } { 36 } m u ^ { 2 }\) After the collision between \(A\) and \(B\), particle \(B\) collides directly with \(C\).
3. Find, in terms of \(u\), the speed of \(C\) immediately after this collision between \(B\) and \(C\).