| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Deriving trajectory equation |
| Difficulty | Moderate -0.8 This is a straightforward projectiles question requiring only standard recall and application of SUVAT equations. Part (i) asks for g=9.8 or 10, part (ii) uses sin(30°)=0.5 to find initial speed from the vertical component, and part (iii) applies horizontal motion with cos(30°). All steps are routine with no problem-solving or novel insight required. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| \(k = \frac{g}{2} = 5\) | B1 | Use the trajectory equation from the formula sheet |
Total: 1 mark
| Answer | Marks | Guidance |
|---|---|---|
| \(V\sin30 = 14\) | M1 | Use the trajectory equation from the formula sheet |
| \(V = 28 \text{ ms}^{-1}\) | A1 (AG) |
Total: 2 marks
| Answer | Marks | Guidance |
|---|---|---|
| \(x = 28\cos30 \times 3\) | M1 | Use horizontal motion. Allow *their* V for M1 |
| \(x = 72.7 \text{ m}\) | A1 |
Total: 2 marks
**Question 1:**
**Part (i):**
$k = \frac{g}{2} = 5$ | B1 | Use the trajectory equation from the formula sheet
Total: 1 mark
---
**Part (ii):**
$V\sin30 = 14$ | M1 | Use the trajectory equation from the formula sheet
$V = 28 \text{ ms}^{-1}$ | A1 (AG) |
Total: 2 marks
---
**Part (iii):**
$x = 28\cos30 \times 3$ | M1 | Use horizontal motion. Allow *their* V for M1
$x = 72.7 \text{ m}$ | A1 |
Total: 2 marks
---1 A small ball is projected from a point $O$ on horizontal ground at an angle of $30 ^ { \circ }$ above the horizontal. At time $t \mathrm {~s}$ after projection the vertically upwards displacement of the ball from $O$ is $\left( 14 t - k t ^ { 2 } \right) \mathrm { m }$, where $k$ is a constant.\\
(i) State the value of $k$.\\
\includegraphics[max width=\textwidth, alt={}, center]{f3a35846-075d-4e03-ba6b-82774ef0e4f8-03_56_1563_495_331}\\
(ii) Show that the initial speed of the ball is $28 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(iii) Find the horizontal displacement of the ball from $O$ when $t = 3$.\\
\hfill \mbox{\textit{CAIE M2 2019 Q1 [5]}}