6 A small smooth ball of mass \(m\), moving on a smooth horizontal surface, hits a smooth vertical wall and rebounds. The coefficient of restitution between the wall and the ball is \(\frac { 3 } { 4 }\). Immediately before the collision, the ball has velocity \(u\) and the angle between the ball's direction of motion and the wall is \(\alpha\). The ball's direction of motion immediately after the collision is at right angles to its direction of motion before the collision, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{eed9842d-cd89-4eb7-b5ba-9380971be196-4_483_344_657_854}

1. Show that \(\tan \alpha = \frac { 2 } { \sqrt { 3 } }\).
2. Find, in terms of \(u\), the speed of the ball immediately after the collision.
3. The force exerted on the ball by the wall acts for 0.1 seconds. Given that \(m = 0.2 \mathrm {~kg}\) and \(u = 4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find the average force exerted by the wall on the ball.