5 Two identical spheres, \(A\) and \(B\), each of mass 4 kg , are moving directly towards each other along the same straight line on a smooth horizontal surface until they collide. Before they collide, the speeds of \(A\) and \(B\) are \(5 \mathrm {~ms} ^ { - 1 }\) and \(3 \mathrm {~ms} ^ { - 1 }\) respectively. Immediately after they collide, the speed of \(A\) is \(2 \mathrm {~ms} ^ { - 1 }\) and its direction of motion has been reversed.

1. 1. Determine the velocity of \(B\) immediately after \(A\) and \(B\) collide.
   2. Show that the coefficient of restitution between \(A\) and \(B\) is \(\frac { 3 } { 4 }\).
   3. Calculate the total loss of kinetic energy due to this collision. Sphere \(B\) goes on to strike a fixed wall directly. As a result of this collision \(B\) moves along the same straight line with a speed of \(4 \mathrm {~ms} ^ { - 1 }\).
2. Find the coefficient of restitution between \(B\) and the wall, stating whether the collision between \(B\) and the wall is perfectly elastic.
3. Determine the magnitude of the impulse that \(B\) exerts on \(A\) the next time that they collide.