M1 June 2011 Q2
2. Particle \(P\) has mass 3 kg and particle \(Q\) has mass 2 kg. The particles are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision, \(P\) has speed 3 m s\(^{-1}\) and \(Q\) has speed 2 m s\(^{-1}\). Immediately after the collision, both particles move in the same direction and the difference in their speeds is 1 m s\(^{-1}\).
(a) Find the speed of each particle after the collision. (5)
(b) Find the magnitude of the impulse exerted on \(P\) by \(Q\). (3)
| Scheme | Marks |
|---|---|
| CLM: \(3 \times 3 - 2 \times 2 = 3v + 2(v + 1)\) | M1 A1 |
| \(v_P = 0.6\) m s\(^{-1}\); \(v_Q = 1.6\) m s\(^{-1}\) | M1A1 (A1 ft) |
| (5) |
| Scheme | Marks |
|---|---|
| \(3(v - 3)\) OR \(2(v + 1 - -2)\) | M1 A1 ft |
| \(= 7.2\) Ns \(= 7.2\) Ns | A1 |
| (3) | |
| (8 marks) |