| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Vector form projectile motion |
| Difficulty | Moderate -0.8 This is a straightforward M1 projectile question using vector notation with standard bookwork throughout: stating assumptions, showing given time of flight using v = u + at, finding range using constant velocity, and finding height at a given horizontal distance. All parts follow routine procedures with no problem-solving insight required, making it easier than average. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Ball is a particle / no spin | B1 | One assumption |
| No air resistance / Only gravity or weight | B1 | Second assumption |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(24.5t-4.9t^2=0\) | M1 | Equation for vertical motion with height zero |
| \(t=0\) or \(t=\frac{24.5}{4.9}=5\text{ s}\) | A1 | Correct equation |
| dM1 | Solving for \(t\) | |
| A1 | Correct time from correct working |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(R=10\times5=50\text{ m}\) | M1 | Use of horizontal component of velocity to find the range |
| A1 | Correct range |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(20=10t\) | M1 | Horizontal equation |
| \(t=2\) | A1 | Time to reach wall |
| \(h=24.5\times2-4.9\times2^2=29.4\text{ m}\) | dM1 | Vertical equation for height with \(u=24.5\) and negative acceleration |
| A1 | Correct height |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| No change as acceleration and initial velocity do not change with the mass | B1 | No change |
| B1 | Explanation |
## Question 6:
**Part (a)**
| Working | Marks | Guidance |
|---------|-------|----------|
| Ball is a particle / no spin | B1 | One assumption |
| No air resistance / Only gravity or weight | B1 | Second assumption |
**Part (b)(i)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $24.5t-4.9t^2=0$ | M1 | Equation for vertical motion with height zero |
| $t=0$ or $t=\frac{24.5}{4.9}=5\text{ s}$ | A1 | Correct equation |
| | dM1 | Solving for $t$ |
| | A1 | Correct time from correct working |
**Part (b)(ii)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $R=10\times5=50\text{ m}$ | M1 | Use of horizontal component of velocity to find the range |
| | A1 | Correct range |
**Part (c)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $20=10t$ | M1 | Horizontal equation |
| $t=2$ | A1 | Time to reach wall |
| $h=24.5\times2-4.9\times2^2=29.4\text{ m}$ | dM1 | Vertical equation for height with $u=24.5$ and negative acceleration |
| | A1 | Correct height |
**Part (d)**
| Working | Marks | Guidance |
|---------|-------|----------|
| No change as acceleration and initial velocity do not change with the mass | B1 | No change |
| | B1 | Explanation |
---6 A ball is hit from horizontal ground with velocity $( 10 \mathbf { i } + 24.5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ where the unit vectors $\mathbf { i }$ and $\mathbf { j }$ are horizontal and vertically upwards respectively.
\begin{enumerate}[label=(\alph*)]
\item State two assumptions that you should make about the ball in order to make predictions about its motion.
\item The path of the ball is shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{7e0585ea-062a-487c-8e39-37a4ed414ff8-5_351_771_705_625}
\begin{enumerate}[label=(\roman*)]
\item Show that the time of flight of the ball is 5 seconds.
\item Find the range of the ball.
\end{enumerate}\item In fact the ball hits a vertical wall that is 20 metres from the initial position of the ball.\\
\includegraphics[max width=\textwidth, alt={}, center]{7e0585ea-062a-487c-8e39-37a4ed414ff8-5_351_403_1466_769}
Find the height of the ball when it hits the wall.
\item If a heavier ball were projected in the same way, would your answers to part (b) of this question change? Explain why.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2005 Q6 [12]}}