6. \(A , B\) and \(C\) are three small spheres of equal radii and masses \(2 m , m\) and \(5 m\) respectively. They are placed in a straight line on a smooth horizontal surface. \(A\) is projected with speed \(6 \mathrm {~ms} ^ { - 1 }\) towards \(B\), which is at rest. When \(A\) hits \(B\) it exerts an impulse of magnitude 8 m Ns on \(B\).

1. Find the speed with which \(B\) starts to move.
2. Show that the speed of \(A\) after it collides with \(B\) is \(2 \mathrm {~ms} ^ { - 1 }\). After travelling \(3 \mathrm {~m} , B\) hits \(C\), which is then travelling towards \(B\) at \(2 \cdot 2 \mathrm {~ms} ^ { - 1 } . C\) is brought to rest by this impact.
3. Show that the direction of \(B\) 's motion is reversed and find its new speed.
4. Find how far \(B\) now travels before it collides with \(A\) again.
5. State a modelling assumption that you have made about the spheres.