M1 January 2011 Q1

1. Two particles \(B\) and \(C\) have mass \(m\) kg and 3 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. The two particles collide directly. Immediately before the collision, the speed of \(B\) is 4 m s\(^{-1}\) and the speed of \(C\) is 2 m s\(^{-1}\). In the collision the direction of motion of \(C\) is reversed and the direction of motion of \(B\) is unchanged. Immediately after the collision, the speed of \(B\) is 1 m s\(^{-1}\) and the speed of \(C\) is 3 m s\(^{-1}\).

Find