| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Velocity direction at specific time/point |
| Difficulty | Standard +0.3 This is a straightforward projectiles question requiring standard techniques: comparing the trajectory equation to the general form to extract initial conditions, then using kinematic equations to find velocity components at a specific angle. The mathematics is routine differentiation and trigonometry with no conceptual surprises, making it slightly easier than average. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration3.02i Projectile motion: constant acceleration model |
| Answer | Marks |
|---|---|
| 5 (i) | xtanα = 0 so α = 0 |
| Answer | Marks |
|---|---|
| V = 10 m s | B1 |
| Answer | Marks |
|---|---|
| [3] | Justification needed |
| Answer | Marks |
|---|---|
| (ii) | dy |
| Answer | Marks |
|---|---|
| y = 15 (below) or –15 | M1 |
| Answer | Marks |
|---|---|
| A1 | Uses Pythagoras |
Question 5:
--- 5 (i) ---
5 (i) | xtanα = 0 so α = 0
gx2
=0.05x2
2V2cos20
–1
V = 10 m s | B1
M1
A1
[3] | Justification needed
Comparison with standard eqn
(ii) | dy
= –0.1x
dx
–0.1x = –tan60
2
y (= –0.05(10tan60) ) = –15
2
v =
2
10 + 2g15
–1
v = 20 m s
OR
y' = 10tan 60
2
(10√3) =2gh
y = –15
2
v =
2 2
10 + (10√3)
–1
v = 20 m s
OR
vcos60 = 10
–1
v = 20 m s
10 3 = 10t
t = 3
3
y = 10 3×
2
y = 15 (below) or –15 | M1
M1
A1
M1
A1
A1
[6]
M1
M1
A1
M1
A1
A1
M1
A1
M1
A1
M1
A1 | Uses Pythagoras
ft candidate’s value (V(i), y)
y' = B’s downward velocity =10√3
Negative, y = –h
Uses Pythagoras
ft candidate’s value (V(i))The equation of the trajectory of a small ball $B$ projected from a fixed point $O$ is
$$y = -0.05x^2,$$
where $x$ and $y$ are, respectively, the displacements in metres of $B$ from $O$ in the horizontal and vertically upwards directions.
\begin{enumerate}[label=(\roman*)]
\item Show that $B$ is projected horizontally, and find its speed of projection. [3]
\item Find the value of $y$ when the direction of motion of $B$ is $60°$ below the horizontal, and find the corresponding speed of $B$. [6]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2014 Q5 [9]}}