7. A particle \(A\) of mass \(m\) is moving with speed \(u\) on a smooth horizontal floor when it collides directly with another particle \(B\), of mass \(3 m\), which is at rest on the floor. The coefficient of restitution between the particles is \(e\). The direction of motion of \(A\) is reversed by the collision.

1. Find, in terms of \(e\) and \(u\),
   1. the speed of \(A\) immediately after the collision,
   2. the speed of \(B\) immediately after the collision. After being struck by \(A\) the particle \(B\) collides directly with another particle \(C\), of mass \(4 m\), which is at rest on the floor. The coefficient of restitution between \(B\) and \(C\) is \(2 e\). Given that the direction of motion of \(B\) is reversed by this collision,
2. find the range of possible values of \(e\),
3. determine whether there will be a second collision between \(A\) and \(B\).