| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2005 |
| Session | January |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projection from elevated point - angle above horizontal |
| Difficulty | Standard +0.3 This is a standard M2 projectiles question requiring systematic application of SUVAT equations with vertical projection from height. While it has multiple parts (4 marks worth), each part follows directly from standard techniques: resolving initial velocity, using s=ut+½at² for time of flight, horizontal distance calculation, and finding velocity components at a given height. The sin α = 3/5 setup makes calculations cleaner. Slightly above average difficulty due to the multi-part nature and need for careful bookkeeping, but no novel problem-solving required. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\uparrow\ u_y = 32 \times \frac{3}{5}\) \((= 19.2)\) | B1 | |
| \(-20 = 19.2t - 4.9t^2\) | M1 A2(1,0) | \(-1\) each error |
| \(t \approx 4.8\) or \(4.77\) (s) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\rightarrow\ u_x = 32 \times \frac{4}{5}\) \((= 25.6)\) | B1 | |
| \(d = 25.6 \times 4.77...\) | M1 | |
| \(\approx 120\) or \(122\) (m) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\uparrow\ v_y^2 = 19.2^2 + 2 \times 9.8 \times 4\) \([v_y^2 = 447.04,\ v_y \approx 21.14]\) | M1 | |
| \(V^2 = 447.04 + 25.6^2\) | M1 A1 | |
| \(V = 33\) or \(33.2 \text{ ms}^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{1}{2}m(V^2 - 32^2) = mg \times 4\) | M1 A1 | |
| \(V^2 = 1102.4\) | M1 | |
| \(V = 33\) or \(33.2 \text{ ms}^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\tan\theta = \frac{21.14}{25.6}\) \(\left(\text{or } \cos\theta = \frac{25.6}{33.2}, \ldots\right)\) | M1 A1ft | ft their components or resultant |
| \(\theta \approx 40°\) or \(39.6°\) | A1 |
## Question 7:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\uparrow\ u_y = 32 \times \frac{3}{5}$ $(= 19.2)$ | B1 | |
| $-20 = 19.2t - 4.9t^2$ | M1 A2(1,0) | $-1$ each error |
| $t \approx 4.8$ or $4.77$ (s) | A1 | |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\rightarrow\ u_x = 32 \times \frac{4}{5}$ $(= 25.6)$ | B1 | |
| $d = 25.6 \times 4.77...$ | M1 | |
| $\approx 120$ or $122$ (m) | A1 | |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\uparrow\ v_y^2 = 19.2^2 + 2 \times 9.8 \times 4$ $[v_y^2 = 447.04,\ v_y \approx 21.14]$ | M1 | |
| $V^2 = 447.04 + 25.6^2$ | M1 A1 | |
| $V = 33$ or $33.2 \text{ ms}^{-1}$ | A1 | |
### Alternative for (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{1}{2}m(V^2 - 32^2) = mg \times 4$ | M1 A1 | |
| $V^2 = 1102.4$ | M1 | |
| $V = 33$ or $33.2 \text{ ms}^{-1}$ | A1 | |
### Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\tan\theta = \frac{21.14}{25.6}$ $\left(\text{or } \cos\theta = \frac{25.6}{33.2}, \ldots\right)$ | M1 A1ft | ft their components or resultant |
| $\theta \approx 40°$ or $39.6°$ | A1 | |7.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{a9e00b5b-3804-4f8d-9cc8-7d1170027726-6_568_1582_360_239}
\end{center}
\end{figure}
A particle $P$ is projected from a point $A$ with speed $32 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of elevation $\alpha$, where $\sin \alpha = \frac { 3 } { 5 }$. The point $O$ is on horizontal ground, with $O$ vertically below $A$ and $O A = 20 \mathrm {~m}$. The particle $P$ moves freely under gravity and passes through a point $B$, which is 16 m above ground, before reaching the ground at the point $C$, as shown in Figure 4.
Calculate
\begin{enumerate}[label=(\alph*)]
\item the time of the flight from $A$ to $C$,
\item the distance $O C$,
\item the speed of $P$ at $B$,
\item the angle that the velocity of $P$ at $B$ makes with the horizontal.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2005 Q7 [15]}}