5. The diagram below shows two spheres \(A\) and \(B\), of equal radii, moving in the same direction on a smooth horizontal surface. Sphere \(A\), of mass 3 kg , is moving with speed \(4 \mathrm {~ms} ^ { - 1 }\) and sphere \(B\), of mass 2 kg , is moving with speed \(10 \mathrm {~ms} ^ { - 1 }\).
\includegraphics[max width=\textwidth, alt={}, center]{b6b77d92-acb6-4cc3-8328-1899ed4a87cd-6_275_972_580_548} Sphere \(B\) is then given an impulse after which it moves in the opposite direction with speed \(6 \mathrm {~ms} ^ { - 1 }\).

1. Calculate the magnitude and direction of the impulse exerted on \(B\). Sphere \(B\) continues to move with speed \(6 \mathrm {~ms} ^ { - 1 }\) so that it collides directly with sphere \(A\). The kinetic energy lost due to the collision is 45 J .
2. Calculate the speed of \(A\) and the speed of \(B\) immediately after the two spheres collide. State the direction in which each sphere is moving relative to its motion immediately before the collision.