Edexcel M2 2012 January — Question 1 4 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2012
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions
TypeVector impulse: find velocity or speed after impulse
DifficultyEasy -1.2 This is a straightforward application of the impulse-momentum theorem (impulse = change in momentum) with vector addition. It requires only direct substitution into a single formula with no problem-solving insight or multi-step reasoning, making it easier than average for A-level.
Spec1.10a Vectors in 2D: i,j notation and column vectors6.03e Impulse: by a force6.03f Impulse-momentum: relation
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]
AnswerMarks
Use of \(m(\mathbf{v} - \mathbf{u}) = \mathbf{I}\)M1
\(0.1 \times (\mathbf{v} - 30\mathbf{i}) = -2\mathbf{i} - 4\mathbf{j}\)A1
Solve for \(\mathbf{v}\): \(0.1\mathbf{v} = 3\mathbf{i} -2\mathbf{i} - 4\mathbf{j} = \mathbf{i} - 4\mathbf{j}\)DM1
\(\mathbf{v} = 10\mathbf{i} - 40\mathbf{j}\)A1
Total: 4 marks
| Use of $m(\mathbf{v} - \mathbf{u}) = \mathbf{I}$ | M1 |
| $0.1 \times (\mathbf{v} - 30\mathbf{i}) = -2\mathbf{i} - 4\mathbf{j}$ | A1 |
| Solve for $\mathbf{v}$: $0.1\mathbf{v} = 3\mathbf{i} -2\mathbf{i} - 4\mathbf{j} = \mathbf{i} - 4\mathbf{j}$ | DM1 |
| $\mathbf{v} = 10\mathbf{i} - 40\mathbf{j}$ | A1 |

**Total: 4 marks**

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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]

\hfill \mbox{\textit{Edexcel M2 2012 Q1 [4]}}
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