5. \section*{Figure 1} A smooth uniform sphere \(S\) of mass \(m\) is moving on a smooth horizontal table. The sphere \(S\) collides with another smooth uniform sphere \(T\), of the same radius as \(S\) but of mass \(k m , k > 1\), which is at rest on the table. The coefficient of restitution between the spheres is \(e\). Immediately before the spheres collide the direction of motion of \(S\) makes an angle \(\theta\) with the line joing their centres, as shown in Fig. 1. Immediately after the collision the directions of motion of \(S\) and \(T\) are perpendicular.

1. Show that \(e = \frac { 1 } { k }\).
   (6) Given that \(k = 2\) and that the kinetic energy lost in the collision is one quarter of the initial kinetic energy,
2. find the value of \(\theta\).
   (6)