CAIE M1 2007 November — Question 2 5 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2007
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeTwo projectiles meeting - vertical motion only
DifficultyModerate -0.5 This is a straightforward kinematics problem requiring students to set up two SUVAT equations (one for each particle) and solve simultaneously for when positions are equal. While it involves multiple steps and careful equation setup, it's a standard textbook exercise with no novel insight required—slightly easier than average due to the direct application of familiar techniques.
Spec3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form
A particle is projected vertically upwards from a point \(O\) with initial speed \(12.5 \text{ m s}^{-1}\). At the same instant another particle is released from rest at a point 10 m vertically above \(O\). Find the height above \(O\) at which the particles meet. [5]
AnswerMarks Guidance
\(s_1 = 12.5t - \frac{1}{2}gt^2, s_2 = \frac{1}{2}gt^2\) or \((12.5 - gt)^2 = 12.5^2 - 2gs_1\) and \((gt)^2 = 2gs_2\)M1 For applying \(s = ut + \frac{1}{2}at^2\) or \((u + at)^2 = u^2 + 2as\) with \(a = \pm g\) (either particle)
A1
[12.5t − ½ gt² + ½ gt² = 10] or \(t = 0.8s\) or \(2s_1 = 25\sqrt{2} - 0.2 s_1 - (20 - 2 s_1)\) (or better)M1 For using \(s_1 + s_2 = 10\)
A1
Height is 6.8mA1ft 5 
$s_1 = 12.5t - \frac{1}{2}gt^2, s_2 = \frac{1}{2}gt^2$ or $(12.5 - gt)^2 = 12.5^2 - 2gs_1$ and $(gt)^2 = 2gs_2$ | M1 | For applying $s = ut + \frac{1}{2}at^2$ or $(u + at)^2 = u^2 + 2as$ with $a = \pm g$ (either particle)
| A1 |
[12.5t − ½ gt² + ½ gt² = 10] or $t = 0.8s$ or $2s_1 = 25\sqrt{2} - 0.2 s_1 - (20 - 2 s_1)$ (or better) | M1 | For using $s_1 + s_2 = 10$
| A1 |
Height is 6.8m | A1ft | 5 | ft for 12.5t − 5t² or 10 − 5t² with candidate's t (requires both M marks)
A particle is projected vertically upwards from a point $O$ with initial speed $12.5 \text{ m s}^{-1}$. At the same instant another particle is released from rest at a point 10 m vertically above $O$. Find the height above $O$ at which the particles meet. [5]

\hfill \mbox{\textit{CAIE M1 2007 Q2 [5]}}
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