Two uniform small smooth spheres \(A\) and \(B\) have equal radii and masses \(5 m\) and \(2 m\) respectively. Sphere \(A\) is moving with speed \(u\) on a smooth horizontal surface when it collides directly with sphere \(B\) which is moving towards it with speed \(2 u\). The coefficient of restitution between the spheres is \(e\).
(i) Show that the speed of \(B\) after the collision is \(\frac{1}{7} u(1+15 e)\) and find an expression for the speed of \(A\).

In the collision, the speed of \(A\) is halved and its direction of motion is reversed.
(ii) Find the value of \(e\).

(iii) For this collision, find the ratio of the loss of kinetic energy of \(A\) to the loss of kinetic energy of \(B\).