| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Deriving trajectory equation |
| Difficulty | Moderate -0.3 This is a standard projectiles question requiring routine application of kinematic equations (x=ut, y=ut-½gt²), elimination of parameter t to find trajectory, and straightforward substitution. The cliff context adds minimal complexity. Slightly easier than average due to simple numbers and direct method application, though the multi-part structure and 8 total marks bring it close to typical difficulty. |
| Spec | 3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| 4(i) | x = 10t or y = gt2 / 2 | B1 |
| y = 15x / 10 – g(x / 10)2 / 2 | M1A1 | Attempts to eliminate t |
| y = 1.5x – 0.05x2 | A1 | |
| Total: | 4 | |
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 4(ii) | 0 = 1.5x – 0.05x2 | M1 |
| x = 30 | A1 | |
| Total: | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| 4(iii) | –14 = 1.5x – 0.05x2 | M1 |
| x = 37.5 | A1 | |
| Total: | 2 |
Question 4:
--- 4(i) ---
4(i) | x = 10t or y = gt2 / 2 | B1
y = 15x / 10 – g(x / 10)2 / 2 | M1A1 | Attempts to eliminate t
y = 1.5x – 0.05x2 | A1
Total: | 4
Question | Answer | Marks | Guidance
--- 4(ii) ---
4(ii) | 0 = 1.5x – 0.05x2 | M1 | Substitute y = 0 into the trajectory equation
x = 30 | A1
Total: | 2
--- 4(iii) ---
4(iii) | –14 = 1.5x – 0.05x2 | M1 | Sets up a quadratic equation and attempts to solve it
x = 37.5 | A1
Total: | 2A particle is projected from a point $O$ on horizontal ground. The initial components of the velocity of the particle are $10 \text{ ms}^{-1}$ horizontally and $15 \text{ ms}^{-1}$ vertically. At time $t$ s after projection, the horizontal and vertically upwards displacements of the particle from $O$ are $x$ m and $y$ m respectively.
\begin{enumerate}[label=(\roman*)]
\item Express $x$ and $y$ in terms of $t$, and hence find the equation of the trajectory of the particle. [4]
\item Show that $d$ is less than $30$. [2]
\item Find the value of $x$ when the particle is $14$ m below the level of $O$. [2]
\end{enumerate}
The horizontal ground is at the top of a vertical cliff. The point $O$ is at a distance $d$ m from the edge of the cliff. The particle is projected towards the edge of the cliff and does not strike the ground before it passes over the edge of the cliff.
\hfill \mbox{\textit{CAIE M2 2017 Q4 [8]}}