Small smooth spheres A and B, of equal radii and of masses \(5\text{ kg}\) and \(3\text{ kg}\) respectively, lie on a smooth horizontal plane. Initially B is at rest and A is moving towards B with speed \(8.5\text{ m s}^{-1}\). The spheres collide and after the collision A continues to move in the same direction but with a quarter of the speed of B.

(a) Find the speed of B after the collision. [3]

(b) Find the loss of kinetic energy of the system due to the collision. [2]