M2 January 2012 Q1
1. A tennis ball of mass 0.1 kg is hit by a racquet. Immediately before being hit, the ball has velocity \(30\mathbf{i}\) m s\(^{-1}\). The racquet exerts an impulse of \((-2\mathbf{i} - 4\mathbf{j})\) N s on the ball. By modelling the ball as a particle, find the velocity of the ball immediately after being hit. (4)
| Scheme | Marks |
|---|---|
| Use of \(\ m(\boldsymbol{v} - \boldsymbol{u}) = \boldsymbol{I}\) | M1 |
| \(0.1 \times (\boldsymbol{v} - 30\mathbf{i}) = -2\mathbf{i} - 4\mathbf{j}\) | A1 |
| Solve for \(\boldsymbol{v}\): \(\ 0.1\boldsymbol{v} = 3\mathbf{i} - 2\mathbf{i} - 4\mathbf{j} = \mathbf{i} - 4\mathbf{j}\) | DM1 |
| \(\boldsymbol{v} = 10\mathbf{i} - 40\mathbf{j}\) | A1 |
| (4 marks) |