Edexcel M4 Specimen — Question 6 14 marks

Exam BoardEdexcel
ModuleM4 (Mechanics 4)
SessionSpecimen
Marks14
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Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeClosest approach of two objects
DifficultyStandard +0.3 This is a standard M4 relative velocity problem with perpendicular motion. Part (a) requires vector subtraction to find relative velocity (routine for M4 students). Part (b) involves setting up position vectors, finding when separation is minimum using calculus or recognizing the closest approach geometry. While it requires multiple steps and careful coordinate work, it follows a well-practiced template for relative motion problems with no novel insights needed.
Spec1.10h Vectors in kinematics: uniform acceleration in vector form

Two horizontal roads cross at right angles. One is directed from south to north, and the other from east to west. A tractor travels north on the first road at a constant speed of 6 m s\(^{-1}\) and at noon is 200 m south of the junction. A car heads west on the second road at a constant speed of 24 m s\(^{-1}\) and at noon is 960 m east of the junction.
  1. Find the magnitude and direction of the velocity of the car relative to the tractor. [6]
  2. Find the shortest distance between the car and the tractor. [8]

Two horizontal roads cross at right angles. One is directed from south to north, and the other from east to west. A tractor travels north on the first road at a constant speed of 6 m s$^{-1}$ and at noon is 200 m south of the junction. A car heads west on the second road at a constant speed of 24 m s$^{-1}$ and at noon is 960 m east of the junction.

\begin{enumerate}[label=(\alph*)]
\item Find the magnitude and direction of the velocity of the car relative to the tractor.
[6]
\item Find the shortest distance between the car and the tractor.
[8]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M4  Q6 [14]}}