| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Apparent wind problems |
| Difficulty | Challenging +1.2 This is a standard M4 apparent wind problem requiring vector addition and simultaneous equations. While it involves multiple steps (setting up two vector equations from the apparent wind conditions, solving for two unknowns), the method is routine for students who have practiced this topic. The geometric setup is straightforward with clear bearings, making it moderately above average difficulty but not requiring novel insight. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| 2 vector triangles with a common side | M1 | |
| Correct and drawn on a single diagram | A1 | |
| Wind is from bearing \(025°\) (N \(25°\) E) | A1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{5}{\sin 25°} = \frac{W}{\sin 40°}\) | M1A1ft | ft on their \(25°\) |
| \(W = \frac{5 \times \sin 40°}{\sin 25°} = 7.6 \ (\text{km h}^{-1})\) | M1A1 | (4) |
## Question 4:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| 2 vector triangles with a common side | M1 | |
| Correct and drawn on a single diagram | A1 | |
| Wind is from bearing $025°$ (N $25°$ E) | A1 | (3) |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{5}{\sin 25°} = \frac{W}{\sin 40°}$ | M1A1ft | ft on their $25°$ |
| $W = \frac{5 \times \sin 40°}{\sin 25°} = 7.6 \ (\text{km h}^{-1})$ | M1A1 | (4) |
---\begin{enumerate}
\item A hiker walking due east at a steady speed of $5 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ notices that the wind appears to come from a direction with bearing 050. At the same time, another hiker moving on a bearing of 320, and also walking at $5 \mathrm {~km} \mathrm {~h} ^ { - 1 }$, notices that the wind appears to come from due north.
\end{enumerate}
Find\\
(a) the direction from which the wind is blowing,\\
(b) the wind speed.\\
\hfill \mbox{\textit{Edexcel M4 2011 Q4 [7]}}