Answer to Question #348886 in Analytic Geometry for Tamzin Jinnah

Question

An aeroplane heads due north at 500km/h. It experiences a 80km/h cross wind flowing in the direction N60 degrees E

find the true velocity of the aeroplane

determine the died of the aeroplane.

Answer 1

a.

$$\vec{v}=500\vec{j}$$ $$\vec{u}=80\sin60\degree \vec{i}+80\cos60\degree\vec{j}$$ $$\vec{v}_{res}=\vec{v}+\vec{u}$$ $$=40\sqrt{3}\vec{i}+540\vec{j}$$ $$|\vec{v}_{res}|=\sqrt{(40\sqrt{3})^2+(540)^2}=20\sqrt{741}(km/h)$$

b.

$$\tan \theta=\dfrac{540}{40\sqrt{3}}=4.5\sqrt{3}$$

$$\theta=\tan^{-1}(4.5\sqrt{3})\approx82.7\degree$$

An aeroplane travels in the direction N $82.7\degree$E at $20\sqrt{741}$ km/h.