| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2014 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Minimum speed to intercept |
| Difficulty | Standard +0.8 This M4 relative velocity problem requires vector decomposition, finding the minimum speed condition (perpendicular velocity of approach), then solving a complex interception problem using the cosine rule and simultaneous equations. Part (b) involves setting up and solving a quadratic from the triangle of velocities, requiring multiple sophisticated steps beyond standard textbook exercises. |
| Spec | 3.02e Two-dimensional constant acceleration: with vectors3.02i Projectile motion: constant acceleration model |
A ship $A$ is travelling at a constant speed of 30 km h$^{-1}$ on a bearing of $050°$. Another ship $B$ is travelling at a constant speed of $v$ km h$^{-1}$ and sets a course to intercept $A$. At 1400 hours $B$ is 20 km from $A$ and the bearing of $A$ from $B$ is $290°$.
\begin{enumerate}[label=(\alph*)]
\item Find the least possible value of $v$. (3)
\end{enumerate}
Given that $v = 32$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the time at which $B$ intercepts $A$. (8)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2014 Q2}}