CAIE M2 2012 June — Question 1 4 marks

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2012
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicProjectiles
TypeBasic trajectory calculations
DifficultyModerate -0.8 This is a straightforward projectiles question requiring standard application of kinematic equations with given initial conditions. Students need to find horizontal and vertical displacements after 2s using basic SUVAT equations, then apply Pythagoras - routine mechanics with no problem-solving insight required.
Spec3.02i Projectile motion: constant acceleration model
1 A particle \(P\) is projected with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) above the horizontal from a point \(O\) on horizontal ground. Calculate the distance \(O P\) at the instant 2 s after projection.
AnswerMarks Guidance
\(OX = (25\cos30°) \times 2\)B1 43.3
\(OY = (25\sin30°) \times 2 - g \times 2^2/2\)B1 5
\(OP^2 = 43.3^2 + 5^2\)M1
\(OP = 43.6\) mA1 [4] [4] 
| $OX = (25\cos30°) \times 2$ | B1 | 43.3 |
| $OY = (25\sin30°) \times 2 - g \times 2^2/2$ | B1 | 5 |
| $OP^2 = 43.3^2 + 5^2$ | M1 | |
| $OP = 43.6$ m | A1 [4] | [4] |
1 A particle $P$ is projected with speed $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $30 ^ { \circ }$ above the horizontal from a point $O$ on horizontal ground. Calculate the distance $O P$ at the instant 2 s after projection.

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