| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile passing through given point |
| Difficulty | Moderate -0.3 This is a standard projectile motion question requiring routine application of kinematic equations at 45° (which simplifies calculations), followed by substitution to find V and solving a quadratic for two x-values. All steps are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| 4(i) | x = (Vcos45)t | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | B1 | Use s=ut+ 1gt2 vertically |
| Answer | Marks | Guidance |
|---|---|---|
| Vcos45 2 Vcos45 | M1 | Attempt to eliminate t |
| Answer | Marks |
|---|---|
| V2 | A1 |
| Answer | Marks |
|---|---|
| 4(ii) | 10×242 |
| Answer | Marks | Guidance |
|---|---|---|
| V2 | M1 | Substitutes x = 18, y = 24 in |
| Answer | Marks |
|---|---|
| V = 31(.0) | A1 |
| Answer | Marks |
|---|---|
| 4(iii) | 10x2 |
| Answer | Marks | Guidance |
|---|---|---|
| 960 | M1 | Put y = 22.5 in part (i) |
| x2 −96x+2160=0 | M1 | Attempt to solve a quadratic |
| Answer | Marks |
|---|---|
| x = 36, 60 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 4:
--- 4(i) ---
4(i) | x = (Vcos45)t | B1 | Use horizontal motion
gt2
y = (Vsin45)t –
2 | B1 | Use s=ut+ 1gt2 vertically
2
( )
Vsin45 x 1 x 2
y= − g
( )
Vcos45 2 Vcos45 | M1 | Attempt to eliminate t
10x2
y=x−
V2 | A1
4
--- 4(ii) ---
4(ii) | 10×242
18=24−
V2 | M1 | Substitutes x = 18, y = 24 in
part (i) equation
V = 31(.0) | A1
2
--- 4(iii) ---
4(iii) | 10x2
22.5=x−
960 | M1 | Put y = 22.5 in part (i)
x2 −96x+2160=0 | M1 | Attempt to solve a quadratic
equation
x = 36, 60 | A1
3
Question | Answer | Marks | GuidanceA small object is projected from a point $O$ with speed $V \text{ ms}^{-1}$ at an angle of $45°$ above the horizontal. At time $t$ after projection, the horizontal and vertically upwards displacements of the object from $O$ are $x \text{ m}$ and $y \text{ m}$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Express $x$ and $y$ in terms of $t$, and hence find the equation of the path. [4]
\end{enumerate}
The object passes through the point with coordinates $(24, 18)$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find $V$. [2]
\item The object passes through two points which are $22.5 \text{ m}$ above the level of $O$. Find the values of $x$ for these points. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2018 Q4 [9]}}