\begin{enumerate} \item Particle \(P\) has mass 3 kg and particle \(Q\) has mass \(m \mathrm {~kg}\). The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of \(P\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(Q\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the collision the direction of motion of \(P\) is unchanged and the direction of motion of \(Q\) is reversed. Immediately after the collision, the speed of \(P\) is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(Q\) is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Find the magnitude of the impulse exerted on \(P\) in the collision.
2. Find the value of \(m\).
   \item A woman travels in a lift. The mass of the woman is 50 kg and the mass of the lift is 950 kg . The lift is being raised vertically by a vertical cable which is attached to the top of the lift. The lift is moving upwards and has constant deceleration of \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). By modelling the cable as being light and inextensible, find