Standard +0.8 This is a relative velocity interception problem requiring vector analysis to find the optimal bearing and time. Students must set up parametric equations, apply the constraint that the boy walks at maximum speed, and minimize time—going beyond routine relative velocity exercises. The optimization aspect and geometric insight needed place it above average difficulty.
A boy enters a large horizontal field and sees a friend 100 m due north. The friend is walking in an easterly direction at a constant speed of 0.75 m s\(^{-1}\). The boy can walk at a maximum speed of 1 m s\(^{-1}\).
Find the shortest time for the boy to intercept his friend and the bearing on which he must travel to achieve this.
[6]
A boy enters a large horizontal field and sees a friend 100 m due north. The friend is walking in an easterly direction at a constant speed of 0.75 m s$^{-1}$. The boy can walk at a maximum speed of 1 m s$^{-1}$.
Find the shortest time for the boy to intercept his friend and the bearing on which he must travel to achieve this.
[6]
\hfill \mbox{\textit{Edexcel M4 2003 Q1 [6]}}