Standard +0.3 This is a standard relative velocity/interception problem requiring vector resolution and trigonometry. While it involves multiple steps (setting up position vectors, using the interception condition, and solving for bearing), the method is routine for M4 students and follows a well-practiced template. The 5 marks reflect computational work rather than conceptual difficulty, making it slightly easier than average.
At noon, a boat \(P\) is on a bearing of \(120°\) from boat \(Q\). Boat \(P\) is moving due east at a constant speed of \(12\) km h\(^{-1}\). Boat \(Q\) is moving in a straight line with a constant speed of \(15\) km h\(^{-1}\) on a course to intercept \(P\). Find the direction of motion of \(Q\), giving your answer as a bearing.
[5]
At noon, a boat $P$ is on a bearing of $120°$ from boat $Q$. Boat $P$ is moving due east at a constant speed of $12$ km h$^{-1}$. Boat $Q$ is moving in a straight line with a constant speed of $15$ km h$^{-1}$ on a course to intercept $P$. Find the direction of motion of $Q$, giving your answer as a bearing.
[5]
\hfill \mbox{\textit{Edexcel M4 2006 Q1 [5]}}