OCR M2 2012 January — Question 1 5 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2012
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeVelocity direction at specific time/point
DifficultyModerate -0.8 This is a straightforward application of standard projectile motion formulas requiring resolution of initial velocity into components, application of v = u + at in each direction, and recombination using Pythagoras and trigonometry. It's a routine M2 question with no problem-solving element, just direct calculation following a well-practiced method.
Spec3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model
1 A particle \(P\) is projected with speed \(40 \mathrm {~ms} ^ { - 1 }\) at an angle of \(35 ^ { \circ }\) above the horizontal from a point \(O\). For the instant 3 s after projection, calculate the magnitude and direction of the velocity of \(P\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(v_x = 40\cos35\)B1 Expect 32.8, need not be evaluated
\(v_y = 40\sin35 - 9.8 \times 3\)B1 Expect −6.46, need not be evaluated
\(v = \sqrt{32.8^2 + 6.46^2}\) or \(\tan\theta = 6.46/32.8\)M1 Use of Pythagoras or relevant trig on \(cv(v_x)\) and \(cv(v_y)\)
\(v = 33.4 \text{ ms}^{-1}\)A1
\(\theta = 11.1°\) below horizontalA1 AEF; allow 11.2 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $v_x = 40\cos35$ | B1 | Expect 32.8, need not be evaluated |
| $v_y = 40\sin35 - 9.8 \times 3$ | B1 | Expect −6.46, need not be evaluated |
| $v = \sqrt{32.8^2 + 6.46^2}$ or $\tan\theta = 6.46/32.8$ | M1 | Use of Pythagoras or relevant trig on $cv(v_x)$ and $cv(v_y)$ |
| $v = 33.4 \text{ ms}^{-1}$ | A1 | |
| $\theta = 11.1°$ below horizontal | A1 | AEF; allow 11.2 |

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1 A particle $P$ is projected with speed $40 \mathrm {~ms} ^ { - 1 }$ at an angle of $35 ^ { \circ }$ above the horizontal from a point $O$. For the instant 3 s after projection, calculate the magnitude and direction of the velocity of $P$.

\hfill \mbox{\textit{OCR M2 2012 Q1 [5]}}
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