| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Apparent wind problems |
| Difficulty | Challenging +1.2 This is a standard M4 relative velocity problem requiring vector addition and simultaneous equations. While it involves multiple steps (setting up two vector equations from apparent wind conditions, solving for components, then finding magnitude and direction), the technique is well-established and follows a predictable pattern. It's harder than routine C1-C3 questions due to the mechanics context and vector manipulation, but easier than problems requiring novel geometric insight or proof. |
| Spec | 1.10c Magnitude and direction: of vectors1.10g Problem solving with vectors: in geometry |
When a woman walks due North at a constant speed of 4 km h$^{-1}$, the wind appears to be blowing from due East. When she runs due South at a constant speed of 8 km h$^{-1}$, the speed of the wind appears to be 20 km h$^{-1}$.
Assuming that the velocity of the wind relative to the earth is constant, find
(i) the speed of the wind,
(ii) the direction from which the wind is blowing.
(6 marks)
---\begin{enumerate}
\item When a woman walks due North at a constant speed of $4 \mathrm {~km} \mathrm {~h} ^ { - 1 }$, the wind appears to be blowing from due East. When she runs due South at a constant speed of $8 \mathrm {~km} \mathrm {~h} ^ { - 1 }$, the speed of the wind appears to be $20 \mathrm {~km} \mathrm {~h} ^ { - 1 }$.
\end{enumerate}
Assuming that the velocity of the wind relative to the earth is constant, find\\
(i) the speed of the wind,\\
(ii) the direction from which the wind is blowing.\\
\hfill \mbox{\textit{Edexcel M4 2015 Q2 [6]}}