Answer
(a) $\vec v_w=\langle 0, 40\rangle$ or $40j$
(b) $\vec v_j=\langle 425, 0\rangle$ or $425i$
(c) $\vec v=\langle 425, 40\rangle$ or $425i+40j$
(d) $427$ mi/h, N $84.6^{\circ}$ E
Work Step by Step
(a) Given that the wind is blowing due north with a speed of 40 mi/h, we have the wind velocity $\vec v_w=\langle 0, 40\rangle$
(b) Given that the jet is due east with a speed of 425 mi/h relative to the air, we have the jet velocity $\vec v_j=\langle 425, 0\rangle$
(c) The true velocity of the jet is the sum of the above vectors: $\vec v=\langle 425, 40\rangle$ mi/h
(d) The true speed can be found as $|\vec v|=\sqrt {(425)^2+(40)^2}\approx427$ mi/h, and the direction $\theta=tan^{-1}\frac{40}{425}\approx5.4^{\circ}$ which is the angle in Quadrant I between the jet true velocity and the x-axis. To find the heading and bearing direction, use $90^{\circ}-5.4^{\circ}=84.6^{\circ}$, we have the direction as N $84.6^{\circ}$ E
