| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Velocity direction at specific time/point |
| Difficulty | Standard +0.3 This is a straightforward projectiles question requiring standard resolution of velocity components and use of kinematic equations. Students must find the angle condition tan(45°)=1 relating horizontal and vertical velocities at t=1.5s, solve for V, then calculate displacements using standard formulae. While it involves multiple steps, all techniques are routine M2 material with no novel insight required, making it slightly easier than average. |
| Spec | 3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Vert comp vel \(= V\sin60 - 1.5g\) | B1 | |
| \(V\cos60 = V\sin60 - 1.5g\) | M1 | \((V\sin60 - 1.5g)/(V\cos60) = \tan45\) |
| \(V = 41(.0)\) | A1 | [3 marks] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(X\ [= (41\cos60) \times 1.5] = 30.7\) m | B1\(\checkmark\) | ft candidate value \((41.0) \times 0.75\); Allow 30.8 |
| \(Y\ [=(41\sin60) \times 1.5 - g1.5^2/2] = 42(.0)\) m | B1\(\checkmark\) | [2 marks] ft candidate value \((41.0) \times 1.3 - 11.25\) |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Vert comp vel $= V\sin60 - 1.5g$ | B1 | |
| $V\cos60 = V\sin60 - 1.5g$ | M1 | $(V\sin60 - 1.5g)/(V\cos60) = \tan45$ |
| $V = 41(.0)$ | A1 | **[3 marks]** |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $X\ [= (41\cos60) \times 1.5] = 30.7$ m | B1$\checkmark$ | ft candidate value $(41.0) \times 0.75$; Allow 30.8 |
| $Y\ [=(41\sin60) \times 1.5 - g1.5^2/2] = 42(.0)$ m | B1$\checkmark$ | **[2 marks]** ft candidate value $(41.0) \times 1.3 - 11.25$ |
---2 A particle $P$ is projected with speed $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $60 ^ { \circ }$ above the horizontal from a point $O$ on horizontal ground. $P$ is moving at an angle of $45 ^ { \circ }$ above the horizontal at the instant 1.5 s after projection.\\
(i) Find $V$.\\
(ii) Hence calculate the horizontal and vertical displacements of $P$ from $O$ at the instant 1.5 s after projection.
\hfill \mbox{\textit{CAIE M2 2015 Q2 [5]}}