| 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 and trajectory derivation. Part (i) involves straightforward substitution into SUVAT equations and eliminating t. Parts (ii) and (iii) require simple algebraic manipulation of the trajectory equation. While multi-part with 8 marks total, each step follows textbook methods with no novel problem-solving or geometric insight required, making it slightly easier than average. |
| 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 $10\,\text{m}\,\text{s}^{-1}$ horizontally and $15\,\text{m}\,\text{s}^{-1}$ 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 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.
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}
\hfill \mbox{\textit{CAIE M2 2017 Q4 [8]}}