5
\includegraphics[max width=\textwidth, alt={}, center]{5cc14ffc-e957-4582-b9d0-182fd89b3df5-08_561_1068_255_500} Two uniform smooth spheres \(A\) and \(B\) of equal radii each have mass \(m\). The two spheres are each moving with speed \(u\) on a horizontal surface when they collide. Immediately before the collision A's direction of motion makes an angle of \(\alpha ^ { \circ }\) with the line of centres, and \(B\) 's direction of motion is perpendicular to that of \(A\) (see diagram). The coefficient of restitution between the spheres is \(e\). Immediately after the collision, \(B\) moves in a direction at right angles to the line of centres.

1. Show that \(\tan \alpha = \frac { 1 + e } { 1 - e }\).
2. Given that \(\tan \alpha = 2\), find the speed of \(A\) after the collision.