Two uniform small smooth spheres \(A\) and \(B\) have equal radii and masses \(2 m\) and \(m\) respectively. Sphere \(A\) is moving with speed \(u\) on a smooth horizontal surface when it collides directly with sphere \(B\) which is at rest. The coefficient of restitution between the spheres is \(\frac{2}{3}\).
(i) Find, in terms of \(u\), the speeds of \(A\) and \(B\) after this collision.

Sphere \(B\) is initially at a distance \(d\) from a fixed smooth vertical wall which is perpendicular to the direction of motion of \(A\). The coefficient of restitution between \(B\) and the wall is \(\frac{1}{2}\).
(ii) Find, in terms of \(d\) and \(u\), the time that elapses between the first and second collisions between \(A\) and \(B\).