Standard +0.3 This is a standard relative velocity/closest approach problem requiring setting up position vectors, finding the distance function, and minimizing it using calculus. While it involves multiple steps (vectors, differentiation, trigonometry for bearing), it follows a well-established method taught in M4 with no novel insight required, making it slightly easier than average.
A cyclist \(P\) is cycling due north at a constant speed of 20 km h\(^{-1}\). At 12 noon another cyclist \(Q\) is due west of \(P\). The speed of \(Q\) is constant at 10 km h\(^{-1}\). Find the course which \(Q\) should set in order to pass as close to \(P\) as possible, giving your answer as a bearing. [5]
A cyclist $P$ is cycling due north at a constant speed of 20 km h$^{-1}$. At 12 noon another cyclist $Q$ is due west of $P$. The speed of $Q$ is constant at 10 km h$^{-1}$. Find the course which $Q$ should set in order to pass as close to $P$ as possible, giving your answer as a bearing. [5]
\hfill \mbox{\textit{Edexcel M4 2005 Q2 [5]}}