4 Two small spheres \(A\) and \(B\) are moving towards each other along a straight line on a smooth horizontal surface. \(A\) has speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(B\) has speed \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) before they collide directly. The direction of motion of \(B\) is reversed in the collision. The speeds of \(A\) and \(B\) after the collision are \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(2.9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively.

1. (a) Show that the direction of motion of \(A\) is unchanged by the collision.
   (b) Calculate the coefficient of restitution between \(A\) and \(B\). The mass of \(B\) is 0.2 kg .
2. Find the mass of \(A\).
   \(B\) continues to move at \(2.9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and strikes a vertical wall at right angles. The wall exerts an impulse of magnitude 0.68 N s on \(B\).
3. Calculate the coefficient of restitution between \(B\) and the wall.