| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile passing through given point |
| Difficulty | Standard +0.3 This is a straightforward projectiles question requiring standard SUVAT equations in two dimensions. Students must resolve motion horizontally (constant velocity) and vertically (constant acceleration), then use simultaneous equations to find angle and speed. The calculations are routine with no conceptual surprises, making it slightly easier than average for A-level mechanics. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| 1(i) | tanθ = 12/20 | M1 |
| θ ( = 30.96) = 31(.0)° | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 0.9 | M1 | Use horizontal motion. Allow their θ for the M mark. |
| V = 25.9 ms−1 | A1 | |
| Total: | 4 |
| Answer | Marks |
|---|---|
| 1(ii) | 0.92 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | M1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| AB ( = 12 – 7.95) = 4.05 m | A1 | Allow AB = 4.06 |
| Total: | 2 |
Question 1:
--- 1(i) ---
1(i) | tanθ = 12/20 | M1 | θ is the angle of projection
θ ( = 30.96) = 31(.0)° | A1
20
Vcos30.96 =
0.9 | M1 | Use horizontal motion. Allow their θ for the M mark.
V = 25.9 ms−1 | A1
Total: | 4
--- 1(ii) ---
1(ii) | 0.92
H = 25.9sin31 × 0.9 – g × ( = 7.948)
2 | M1 | 1
Use s = ut + at2 vertically. H is the height above the ground.
2
Allow their V and θ for the M mark.
AB ( = 12 – 7.95) = 4.05 m | A1 | Allow AB = 4.06
Total: | 2\includegraphics{figure_1}
A small ball $B$ is projected from a point $O$ on horizontal ground towards a point $A$ 12 m above the ground. 0.9 s after projection $B$ has travelled a horizontal distance of 20 m and is vertically below $A$ (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Find the angle and the speed of projection of $B$. [4]
\item Calculate the distance $AB$ when $B$ is vertically below $A$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2018 Q1 [6]}}