| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Mechanics (Further AS Paper 2 Mechanics) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Free fall: time or distance |
| Difficulty | Standard +0.3 This is a standard SUVAT problem with vertical motion under gravity, requiring straightforward application of kinematic equations across multiple parts. Part (a) uses basic free fall equations, part (b) compares final position to a threshold, and part (c) asks for a standard modelling assumption discussion. While it's a multi-part question requiring careful calculation, it involves routine mechanics techniques without novel problem-solving or geometric insight, making it slightly easier than the average A-level question. |
| Spec | 3.02h Motion under gravity: vector form6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{1}{2}mv^2 = mgh \Rightarrow \frac{1}{2}(75)v^2 = 75g(25)\) | M1 | Forms correct equation applying conservation of energy with KE and PE; substituting values given |
| \(v^2 = 50g = 490\), so \(v = 22\) m s\(^{-1}\) (2sf) | A1 | Solves correctly to obtain \(v\); must be rounded correctly to 2 significant figures |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{\lambda x^2}{2l} = mgh \Rightarrow \frac{3200x^2}{2(25)} = 75(9.8)(25+x)\) | M1 | Forms expressions for EPE and PE |
| \(64x^2 - 735x - 18375 = 0\), \(x = 23.6\ldots\) | A1 | Obtains fully correct expressions |
| \(23.6 + 25 = 48.6\) m | M1 | Solves three-term quadratic or substitutes correct distances for total length of 50 m into both expressions |
| \(48.6\) m \(< 50\) m | A1 | Obtains correct maximum extension or correct values for the two energies |
| Dominic does not get wet | E1F | Compares their results and concludes Dominic does not get wet |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Dominic has size so distance descended would be greater than 48.6 m | E1 | Comments that Dominic has size and considers effect this might have on distance fallen |
| He might get wet if he was taller than 1.4 m | E1F | States clearly whether Dominic does or does not get wet, justifying conclusion |
## Question 7(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{1}{2}mv^2 = mgh \Rightarrow \frac{1}{2}(75)v^2 = 75g(25)$ | M1 | Forms correct equation applying conservation of energy with KE and PE; substituting values given |
| $v^2 = 50g = 490$, so $v = 22$ m s$^{-1}$ (2sf) | A1 | Solves correctly to obtain $v$; must be rounded correctly to 2 significant figures |
## Question 7(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{\lambda x^2}{2l} = mgh \Rightarrow \frac{3200x^2}{2(25)} = 75(9.8)(25+x)$ | M1 | Forms expressions for EPE and PE |
| $64x^2 - 735x - 18375 = 0$, $x = 23.6\ldots$ | A1 | Obtains fully correct expressions |
| $23.6 + 25 = 48.6$ m | M1 | Solves three-term quadratic or substitutes correct distances for total length of 50 m into both expressions |
| $48.6$ m $< 50$ m | A1 | Obtains correct maximum extension or correct values for the two energies |
| Dominic does not get wet | E1F | Compares their results and concludes Dominic does not get wet |
## Question 7(c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Dominic has size so distance descended would be greater than 48.6 m | E1 | Comments that Dominic has size and considers effect this might have on distance fallen |
| He might get wet if he was taller than 1.4 m | E1F | States clearly whether Dominic does or does not get wet, justifying conclusion |7
\begin{enumerate}[label=(\alph*)]
\item Find Dominic's speed at the point when the cord initially becomes taut.\\
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\item Determine whether or not Dominic enters the river and gets wet.\\
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\item One limitation of this model is that Dominic is not a particle.\\
Explain the effect of revising this assumption on your answer to part (b).\\
\includegraphics[max width=\textwidth, alt={}, center]{1b79a789-c003-46c9-9235-254c1d8a0501-12_2492_1721_217_150}
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Write the question numbers in the left-hand margin.
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Write the question numbers in the left-hand margin.
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\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2018 Q7 [9]}}