2 Two uniform smooth spheres \(A\) and \(B\), of equal radius and equal mass, are moving towards each other on a horizontal surface. Immediately before they collide, \(A\) has speed \(0.3 \mathrm {~ms} ^ { - 1 }\) along the line of centres and \(B\) has speed \(0.6 \mathrm {~ms} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) to the line of centres (see diagram).
\includegraphics[max width=\textwidth, alt={}, center]{dfe477d4-eae6-40e1-b704-1a97485f4c7e-2_302_1013_1247_502} After the collision, the direction of motion of \(B\) is at right angles to its original direction of motion. Find

1. the speed of \(B\) after the collision,
2. the speed and direction of motion of \(A\) after the collision,
3. the coefficient of restitution between \(A\) and \(B\).