| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Apparent wind problems |
| Difficulty | Standard +0.3 This is a standard M4 relative velocity problem requiring the relationship v_apparent = v_wind - v_observer. Students set up two vector equations and solve simultaneously for the unknowns. While it involves multiple steps and vector algebra, it follows a well-practiced template from the M4 syllabus with no novel insight required, making it slightly easier than average. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation3.02e Two-dimensional constant acceleration: with vectors |
[In this question $\mathbf{i}$ and $\mathbf{j}$ are horizontal unit vectors due east and due north respectively.]
A man cycling at a constant speed $u$ on horizontal ground finds that, when his velocity is $u\mathbf{j}$ m s$^{-1}$, the velocity of the wind appears to be $v(3\mathbf{i} - 4\mathbf{j})$ m s$^{-1}$, where $v$ is a constant. When the velocity of the man is $\frac{u}{5}(-3\mathbf{i} + 4\mathbf{j})$ m s$^{-1}$, he finds that the velocity of the wind appears to be $w\mathbf{i}$ m s$^{-1}$, where $w$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Show that $v = \frac{u}{20}$, and find $w$ in terms of $u$. [5]
\item Find, in terms of $u$, the true velocity of the wind. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2005 Q2 [7]}}