| Exam Board | AQA |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Basic trajectory calculations |
| Difficulty | Standard +0.3 This is a straightforward mechanics question requiring standard SUVAT equations for vertical motion (part a) and basic projectile motion with a small angle variation (part b). The calculations are routine: using v² = u² + 2as to verify the height claim, stating standard modeling assumptions, then resolving initial velocity at 11° to find the reduced vertical component. All techniques are standard A-level mechanics with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks |
|---|---|
| 19(a)(i) | Substitutes three of the four |
| Answer | Marks | Guidance |
|---|---|---|
| the substituted values | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| AG | 2.1 | R1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 19(a)(ii) | States one valid assumption |
| Answer | Marks | Guidance |
|---|---|---|
| ground | 3.5b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| ground | 3.5b | E1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 19(b) | States or uses 7cos11 for the |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 2.2a | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| v = 0 and a = – 9.8 | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Accept any variable for k | 1.1b | A1 |
| Obtains AWRT 2.4 | 1.1b | A1 |
| Subtotal | 4 | |
| Question 19 Total | 8 | |
| Q | Marking instructions | AO |
Question 19:
--- 19(a)(i) ---
19(a)(i) | Substitutes three of the four
given values into v2 =u2 +2as
Condone inconsistent signs for
the substituted values | 3.1b | M1 | v=0, u =7,a =−9.8
Using v2 =u2 +2as then:
0=49−2(9.8)h
49
h= =2.5m
2(9.8)
The claim is correct
Completes reasoned argument
to obtain the correct fourth value
and concludes the claim is
correct
Must have clearly stated three
out of the following four
v=0
u =7
a=−9.8 or −g
s =2.5
Allow a consistent swapping of
signs
AG | 2.1 | R1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 19(a)(ii) ---
19(a)(ii) | States one valid assumption
from:
• No air resistance
• The ball is a particle
• The ball is shot from the
ground | 3.5b | E1 | • The ball experiences no air
resistance
• Ball projected from ground
level
States a second valid
assumption from
• No air resistance
• The ball is a particle
• The ball is shot from the
ground | 3.5b | E1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 19(b) ---
19(b) | States or uses 7cos11 for the
vertical component of velocity
OE | 2.2a | B1 | s =k
u =7cos11
v =0
a =−9.8
v2 =u2 +2as
0=49cos 2 11+2(−9.8)k
k = 2.4
Uses v2 =u2 +2aswith u = their
vertical component of velocity,
v = 0 and a = – 9.8 | 3.1b | M1
Obtains
0=49cos 2 11+2(−9.8)k
Accept any variable for k | 1.1b | A1
Obtains AWRT 2.4 | 1.1b | A1
Subtotal | 4
Question 19 Total | 8
Q | Marking instructions | AO | Marks | Typical solutionIn this question use $g = 9.8$ m s$^{-2}$
A toy shoots balls upwards with an initial velocity of 7 m s$^{-1}$
The advertisement for this toy claims the balls can reach a maximum height of 2.5 metres from the ground.
\begin{enumerate}[label=(\alph*)]
\item Suppose that the toy shoots the balls vertically upwards.
\begin{enumerate}[label=(\roman*)]
\item Verify the claim in the advertisement.
[2 marks]
\item State two modelling assumptions you have made in verifying this claim.
[2 marks]
\end{enumerate}
\item In fact the toy shoots the balls anywhere between 0 and 11 degrees from the vertical.
The range of maximum heights, $h$ metres, above the ground which can be reached by the balls may be expressed as
$$k \leq h \leq 2.5$$
Find the value of $k$
[4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 2 2024 Q19 [8]}}