| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | March |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projection from elevated point - angle below horizontal or horizontal |
| Difficulty | Moderate -0.3 This is a straightforward projectile motion problem with downward projection. Part (i) requires solving a quadratic equation using standard kinematic equations (s = ut + ½at²), and part (ii) involves finding horizontal and vertical velocity components then combining them. While it requires careful sign handling and multiple steps (7 marks total), the techniques are standard and well-practiced in M2, making it slightly easier than average but not trivial due to the computational work involved. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks |
|---|---|
| 3(i) | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | M1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 5t2 + 10 3 t – 30 = 0 | M1 | Sets up a quadratic equation and attempts |
| Answer | Marks | Guidance |
|---|---|---|
| t = 1.27 | A1 | |
| Total: | 3 | |
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 3(ii) | v2 = (20sin60)2 + 2g x 30 (hence v = 30) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| tanθ = 30/(20cos60) | M1 | |
| V = 31.6 ms–1 | A1 | |
| θ = 71.6° with the horizontal | A1 | Or 18.4° with the downward vertical |
| Total: | 4 | |
| Question | Answer | Marks |
Question 3:
--- 3(i) ---
3(i) | 1
30 = (20sin60)t + gt2
2 | M1 | 1
Uses s = ut + at2 vertically
2
5t2 + 10 3 t – 30 = 0 | M1 | Sets up a quadratic equation and attempts
to solve it
t = 1.27 | A1
Total: | 3
Question | Answer | Marks | Guidance
--- 3(ii) ---
3(ii) | v2 = (20sin60)2 + 2g x 30 (hence v = 30) | B1 | Uses v2 = u2 + 2as vertically
V = 302 + (20cos60)2 or
tanθ = 30/(20cos60) | M1
V = 31.6 ms–1 | A1
θ = 71.6° with the horizontal | A1 | Or 18.4° with the downward vertical
Total: | 4
Question | Answer | Marks | GuidanceA particle $P$ is projected with speed $20 \text{ m s}^{-1}$ at an angle of $60°$ below the horizontal, from a point $O$ which is $30 \text{ m}$ above horizontal ground.
\begin{enumerate}[label=(\roman*)]
\item Calculate the time taken by $P$ to reach the ground. [3]
\item Calculate the speed and direction of motion of $P$ immediately before it reaches the ground. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2017 Q3 [7]}}