6 Two identical spheres, \(A\) and \(B\), each of mass \(m \mathrm {~kg}\), are moving directly towards each other along the same straight line on a smooth horizontal surface until they collide. Just before they collide, the speeds of \(A\) and \(B\) are \(20 \mathrm {~ms} ^ { - 1 }\) and \(10 \mathrm {~ms} ^ { - 1 }\) respectively. The coefficient of restitution between \(A\) and \(B\) is \(e\).

1. By finding, in terms of \(e\), an expression for the velocity of \(B\) after the collision, show that the direction of motion of \(B\) is reversed by the collision. After the collision between \(A\) and \(B\), which is not perfectly elastic, \(B\) goes on to collide directly with a fixed, vertical wall. The coefficient of restitution between \(B\) and the wall is \(\frac { 2 } { 5 } e\). After the collision between \(B\) and the wall, there are no further collisions between \(A\) and \(B\).
2. Determine the range of possible values of \(e\).
   \(7 \quad\) A body \(B\) of mass 1.5 kg is moving along the \(x\)-axis. At the instant that it is at the origin, \(O\), its velocity is \(u \mathrm {~ms} ^ { - 1 }\) in the positive \(x\)-direction. At any instant, the resistance to the motion of \(B\) is modelled as being directly proportional to \(v ^ { 2 }\) where \(v \mathrm {~ms} ^ { - 1 }\) is the velocity of \(B\) at that instant. The resistance to motion is the only horizontal force acting on \(B\). At an instant when \(B\) 's velocity is \(2 \mathrm {~ms} ^ { - 1 }\), the resistance to its motion is 24 N .