12.
[0pt] [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors in a horizontal plane.]
A smooth uniform sphere \(A\) has mass 0.2 kg and another smooth uniform sphere \(B\), with the same radius as \(A\), has mass 0.4 kg . The spheres are moving on a smooth horizontal surface when they collide obliquely. Immediately before the collision, the velocity of \(A\) is \(( 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(B\) is \(( - 4 \mathbf { i } - \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) At the instant of collision, the line joining the centres of the spheres is parallel to \(\mathbf { i }\) The coefficient of restitution between the spheres is \(\frac { 3 } { 7 }\)

1. Find the velocity of \(A\) immediately after the collision.
2. Find the magnitude of the impulse received by \(A\) in the collision.
3. Find, to the nearest degree, the size of the angle through which the direction of motion of \(A\) is deflected as a result of the collision.