Answer to Question #335035 in Math for Busi

Question

An aeroplane heads due north at 500 km/h. It experiences a 80 km/h crosswind flowing in

the direction N60^°E.

(a) Find the true velocity of the aeroplane.

Answer 1

$$\vec{v}=500\vec{j}$$

$$\vec{u}=80\sin60\degree \vec{i}+80\cos60\degree\vec{j}$$

$$\vec{v}_{res}=\vec{v}+\vec{u}$$

$$=40\sqrt{3}\vec{i}+540\vec{j}$$

$$|\vec{v}_{res}|=\sqrt{(40\sqrt{3})^2+(540)^2}=20\sqrt{741}(km/h)$$

$$\tan \theta=\dfrac{40\sqrt{3}}{540}=\dfrac{2\sqrt{3}}{27}$$

$$\theta=\tan^{-1}\dfrac{2\sqrt{3}}{27}\approx7.3111\degree$$

$20\sqrt{741}$ km/h in the direction $N(\tan^{-1}\dfrac{2\sqrt{3}}{27})\degree E.$

$544.4263$ km/h in the direction $N(7.31)\degree E.$