7 Two small spheres \(A\) and \(B\), with masses 0.3 kg and \(m \mathrm {~kg}\) respectively, lie at rest on a smooth horizontal surface. \(A\) is projected directly towards \(B\) with speed \(6 \mathrm {~ms} ^ { - 1 }\) and hits \(B\). The direction of motion of \(A\) is reversed in the collision. The speeds of \(A\) and \(B\) after the collision are \(1 \mathrm {~ms} ^ { - 1 }\) and \(3 \mathrm {~ms} ^ { - 1 }\) respectively. The coefficient of restitution between \(A\) and \(B\) is \(e\).

1. Show that \(m = 0.7\).
2. Find \(e\). B continues to move at \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and strikes a vertical wall at right angles. The coefficient of restitution between \(B\) and the wall is \(f\).
3. Find the range of values of \(f\) for which there will be a second collision between \(A\) and \(B\).
4. Find, in terms of \(f\), the magnitude of the impulse that the wall exerts on \(B\).
5. Given that \(f = \frac { 3 } { 4 }\), calculate the final speeds of \(A\) and \(B\), correct to 1 decimal place.