Two uniform smooth spheres, \(A\) and \(B\), of equal radii are on a horizontal surface. They have masses of \(m\) and \(k m\) respectively. Sphere \(A\) is moving with speed \(u\) at an angle \(\alpha\) with the line of centres when it collides with sphere \(B\) which is stationary. Immediately after the collision, sphere \(A\) moves with speed \(v\) at an angle \(2 \alpha\) with the line of centres (see diagram).

It is given that \(\tan \alpha=\frac{3}{4}\). (a) Find \(v\) in terms of \(u\).

(b) Find the coefficient of restitution between the spheres in terms of \(k\).

(c) Find the range of possible values of \(k\).