M2 January 2011 Q2
2. A particle of mass 2 kg is moving with velocity \((5\mathbf{i} + \mathbf{j})\) m s\(^{-1}\) when it receives an impulse of \((-6\mathbf{i} + 8\mathbf{j})\) N s. Find the kinetic energy of the particle immediately after receiving the impulse. (5)
| Scheme | Marks |
|---|---|
| \(\mathbf{I} = (-6\mathbf{i} + 8\mathbf{j}) = 2\left(\mathbf{v} - (5\mathbf{i} + \mathbf{j})\right)\) | M1A1 |
| \(-3\mathbf{i} + 4\mathbf{j} = \mathbf{v} - 5\mathbf{i} - \mathbf{j}\) | |
| \(\mathbf{v} = 2\mathbf{i} + 5\mathbf{j}\) | A1 |
| \(\text{KE} = \dfrac{1}{2} \times 2 \times |v|^2 = \left(\sqrt{2^2 + 5^2}\right)^2 = 29\ (\text{J})\) | M1 A1 |
| (5 marks) |