Standard +0.8 This is a relative velocity problem requiring vector decomposition and simultaneous equations. Students must set up two vector equations from the apparent wind directions, then solve for the true wind velocity components. While the concepts are standard M4 material, the problem requires careful geometric reasoning about relative velocities and systematic algebraic manipulation, making it moderately challenging but not exceptional for this module.
Boat \(A\) is sailing due east at a constant speed of 10 km h\(^{-1}\). To an observer on \(A\), the wind appears to be blowing from due south. A second boat \(B\) is sailing due north at a constant speed of 14 km h\(^{-1}\). To an observer on \(B\), the wind appears to be blowing from the south west. The velocity of the wind relative to the earth is constant and is the same for both boats.
Find the velocity of the wind relative to the earth, stating its magnitude and direction.
[7]
Boat $A$ is sailing due east at a constant speed of 10 km h$^{-1}$. To an observer on $A$, the wind appears to be blowing from due south. A second boat $B$ is sailing due north at a constant speed of 14 km h$^{-1}$. To an observer on $B$, the wind appears to be blowing from the south west. The velocity of the wind relative to the earth is constant and is the same for both boats.
Find the velocity of the wind relative to the earth, stating its magnitude and direction.
[7]
\hfill \mbox{\textit{Edexcel M4 2003 Q2 [7]}}