7. Three particles \(A , B\) and \(C\), each of mass \(m\), lie at rest in a straight line \(L\) on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). Particles \(A\) and \(B\) are projected directly towards each other with speeds \(5 u\) and \(4 u\) respectively. Particle \(C\) is projected directly away from \(B\) with speed \(3 u\). In the subsequent motion, \(A , B\) and \(C\) move along \(L\). Particles \(A\) and \(B\) collide directly. The coefficient of restitution between \(A\) and \(B\) is \(e\).
- Find (i) the speed of \(A\) immediately after the collision,
(ii) the speed of \(B\) immediately after the collision.
Given that the direction of motion of \(A\) is reversed in the collision between \(A\) and \(B\), and that there is no collision between \(B\) and \(C\), - find the set of possible values of \(e\).