M1 January 2005 Q1
1. A particle \(P\) of mass 1.5 kg is moving along a straight horizontal line with speed 3 m s\(^{-1}\). Another particle \(Q\) of mass 2.5 kg is moving, in the opposite direction, along the same straight line with speed 4 m s\(^{-1}\). The particles collide. Immediately after the collision the direction of motion of \(P\) is reversed and its speed is 2.5 m s\(^{-1}\).
(a) Calculate the speed of \(Q\) immediately after the impact. (3)
(b) State whether or not the direction of motion of \(Q\) is changed by the collision. (1)
(c) Calculate the magnitude of the impulse exerted by \(Q\) on \(P\), giving the units of your answer. (3)
| Scheme | Marks |
|---|---|
| CLM: \(1.5 \times 3 - 2.5 \times 4 = -1.5 \times 2.5 + 2.5 \times v\) | M1 A1 |
| \(\Rightarrow v = -0.7\) m s\(^{-1}\) so speed \(= 0.7\) m s\(^{-1}\) | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| Direction of \(Q\) unchanged | A1ft |
| (1) |
| Scheme | Marks |
|---|---|
| Impulse \(= 1.5(3 + 2.5)\) | M1 |
| \(= 8.25\), Ns | A1, B1 |
| (3) | |
| (7 marks) |