Answer to Question #335036 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.

(b) Determine the speed of the aeroplane. (Leave your answer in terms of square root) (3)

Answer 1

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

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

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

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

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