3 Three uniform small spheres \(A , B\) and \(C\) have equal radii and masses \(5 m , 5 m\) and \(3 m\) respectively. The spheres are at rest on a smooth horizontal surface, in a straight line, with \(B\) between \(A\) and \(C\). The coefficient of restitution between each pair of spheres is \(e\). Sphere \(A\) is projected directly towards \(B\) with speed \(u\).

1. Show that the speed of \(A\) after its collision with \(B\) is \(\frac { 1 } { 2 } u ( 1 - e )\) and find the speed of \(B\).
   Sphere \(B\) now collides with sphere \(C\). Subsequently there are no further collisions between any of the spheres.
2. Find the set of possible values of \(e\).