5. A smooth uniform sphere \(A\) has mass \(2 m \mathrm {~kg}\) and another smooth uniform sphere \(B\), with the same radius as \(A\), has mass \(m \mathrm {~kg}\). The spheres are moving on a smooth horizontal plane when they collide. At the instant of collision the line joining the centres of the spheres is parallel to j. Immediately after the collision, the velocity of \(A\) is ( \(3 \mathbf { i } - \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(B\) is \(( 2 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). The coefficient of restitution between the spheres is \(\frac { 1 } { 2 }\).

1. Find the velocities of the two spheres immediately before the collision.
2. Find the magnitude of the impulse in the collision.
3. Find, to the nearest degree, the angle through which the direction of motion of \(A\) is deflected by the collision.