M2 June 2013 Q1
1. A particle \(P\) of mass 2 kg is moving with velocity \((\mathbf{i} - 4\mathbf{j})\) m s\(^{-1}\) when it receives an impulse of \((3\mathbf{i} + 6\mathbf{j})\) N s.
Find the speed of \(P\) immediately after the impulse is applied. (5)
| Scheme | Marks |
|---|---|
| Use of \(\mathbf{I} = m\mathbf{v} - m\mathbf{u}\) | M1 |
| \(2\mathbf{v} = (3\mathbf{i} + 6\mathbf{j}) + 2(\mathbf{i} - 4\mathbf{j})\) | A1 |
| \(\mathbf{v} = 2.5\mathbf{i} - \mathbf{j}\) | A1 |
| Speed \(= \sqrt{2.5^2 + 1^2} = \sqrt{7.25}\ (= 2.69\ (\text{m s}^{-1}))\) | M1 A1 |
| (5 marks) |
Notes
M1 Must be subtracting. Condone subtraction in the wrong order
A1 Correct unsimplified equation (\(= 5\mathbf{i} - 2\mathbf{j}\))
M1 Use of correct Pythagoras with their \(\mathbf{v}\)
A1 Exact form or 2s.f. or better. Watch out for fortuitous answers from \(2.5\mathbf{i} + \mathbf{j}\).