6 Three particles \(A , B\) and \(C\) are in a straight line on a smooth horizontal surface. The particles have masses \(0.2 \mathrm {~kg} , 0.4 \mathrm {~kg}\) and 0.6 kg respectively. \(B\) is at rest. \(A\) is projected towards \(B\) with a speed of \(1.8 \mathrm {~ms} ^ { - 1 }\) and collides with \(B\). The coefficient of restitution between \(A\) and \(B\) is \(\frac { 1 } { 3 }\).

1. Show that the speed of \(B\) after the collision is \(0.8 \mathrm {~ms} ^ { - 1 }\) and find the speed of \(A\) after the collision.
   \(C\) is moving with speed \(0.2 \mathrm {~ms} ^ { - 1 }\) in the same direction as \(B\). Particle \(B\) subsequently collides with \(C\). The coefficient of restitution between \(B\) and \(C\) is \(e\).
2. Find the set of values for \(e\) such that \(B\) does not collide again with \(A\).