| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile clearing obstacle |
| Difficulty | Standard +0.3 This is a straightforward projectile motion problem requiring standard equations to find the height at a given horizontal distance, then compare to the crossbar height. The calculation is routine with clearly given values, though it requires careful substitution into y = x tan θ - gx²/(2u²cos²θ). Slightly above average difficulty due to the numerical work and need to state an assumption, but still a standard M1 exercise. |
| Spec | 3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Equate \(\mathbf{i}\) and \(\mathbf{j}\) components of \(\mathbf{v}\) | M1 | The candidate recognises that the \(\mathbf{i}\) and \(\mathbf{j}\) components must be equal |
| \(16-t^2=31-8t\) | A1 | An equation is formed |
| \(t^2-8t+15=0\) | ||
| \((t-3)(t-5)=0\) | ||
| \(t=3\) or \(5\) | A1 | May be implied by later working |
| When \(t=3\), \(\mathbf{v}=7\mathbf{i}+7\mathbf{j}\) | B1 | |
| Speed when \(t=3\) is \(7\sqrt{2}=9.9\) m s\(^{-1}\) | B1 | |
| The values of the \(\mathbf{i}\) and \(\mathbf{j}\) components must both be positive for the bearing to be \(045°\) | B1 | Dependent on A1 for \(t=3\) or \(5\). Awarded if speed for \(t=5\) not included (since \(t=5 \Rightarrow \mathbf{v}=-9\mathbf{i}-9\mathbf{j}\) and bearing is \(225°\)) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| The \(\mathbf{i}\) and \(\mathbf{j}\) components of \(\mathbf{v}\) must be equal | M1 | Candidate recognises \(\mathbf{i}\) and \(\mathbf{j}\) components must be equal |
| The \(\mathbf{i}\) and \(\mathbf{j}\) components of \(\mathbf{v}\) must both be positive for bearing to be \(045°\) | B1 | Can be demonstrated by convincing diagram including \(45°\) or suitable argument |
| At least one value of \(t\) is substituted | A1 | Trial and error is used |
| \(t=3\) | A1 | \(t=3\) is found by trial and error |
| When \(t=3\), \(\mathbf{v}=7\mathbf{i}+7\mathbf{j}\) | B1 | |
| Speed when \(t=3\) is \(7\sqrt{2}=9.9\) m s\(^{-1}\) | B1 |
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Equate $\mathbf{i}$ and $\mathbf{j}$ components of $\mathbf{v}$ | M1 | The candidate recognises that the $\mathbf{i}$ and $\mathbf{j}$ components must be equal |
| $16-t^2=31-8t$ | A1 | An equation is formed |
| $t^2-8t+15=0$ | | |
| $(t-3)(t-5)=0$ | | |
| $t=3$ or $5$ | A1 | May be implied by later working |
| When $t=3$, $\mathbf{v}=7\mathbf{i}+7\mathbf{j}$ | B1 | |
| Speed when $t=3$ is $7\sqrt{2}=9.9$ m s$^{-1}$ | B1 | |
| The values of the $\mathbf{i}$ and $\mathbf{j}$ components must both be positive for the bearing to be $045°$ | B1 | Dependent on A1 for $t=3$ or $5$. Awarded if speed for $t=5$ not included (since $t=5 \Rightarrow \mathbf{v}=-9\mathbf{i}-9\mathbf{j}$ and bearing is $225°$) |
### Alternative (Trial and Error):
| Answer | Marks | Guidance |
|--------|-------|----------|
| The $\mathbf{i}$ and $\mathbf{j}$ components of $\mathbf{v}$ must be equal | M1 | Candidate recognises $\mathbf{i}$ and $\mathbf{j}$ components must be equal |
| The $\mathbf{i}$ and $\mathbf{j}$ components of $\mathbf{v}$ must both be positive for bearing to be $045°$ | B1 | Can be demonstrated by convincing diagram including $45°$ or suitable argument |
| At least one value of $t$ is substituted | A1 | Trial and error is used |
| $t=3$ | A1 | $t=3$ is found by trial and error |
| When $t=3$, $\mathbf{v}=7\mathbf{i}+7\mathbf{j}$ | B1 | |
| Speed when $t=3$ is $7\sqrt{2}=9.9$ m s$^{-1}$ | B1 | |
---3 A football is kicked with speed $31 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $20 ^ { \circ }$ to the horizontal. It travels towards the goal which is 50 m away. The height of the crossbar of the goal is 2.44 m .\\
(i) Does the ball go over the top of the crossbar? Justify your answer.\\
(ii) State one assumption that you made in answering part (i).
\hfill \mbox{\textit{OCR MEI M1 Q3 [7]}}