7 Two small uniform smooth spheres A and B , of masses 2 kg and 3 kg respectively, are moving in opposite directions along the same straight line towards each other on a smooth horizontal surface. Sphere \(A\) has speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and B has speed \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) before they collide. The coefficient of restitution between A and B is e .

1. Show that the velocity of B after the collision, in the original direction of motion of A , is \(\frac { 1 } { 5 } ( 1 + 6 e ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and find a similar expression for the velocity of A after the collision.
2. The following three parts are independent of each other, and each considers a different scenario regarding the collision between A and B .
   1. In the collision between A and B the spheres coalesce to form a combined body C . State the speed of C after the collision.
   2. In the collision between A and B the direction of motion of A is reversed. Find the range of possible values of e .
   3. The total loss in kinetic energy due to the collision is 3 J . Determine the value of e.