Question

A plane flies with a velocity of 100km/hr to n a direction N60°E. Find its velocity in the easterly and northerly directions

Answer 1

Here the length of velocity vector is $|\mathbf{v}| = 100\, km/h$.

A projection of the velocity $\mathbf{v}$ in the easterly direction is

$$v_E = |\mathbf{v}|\cos30\degree = 100\cdot \dfrac{\sqrt{2}}{2}\approx 70.71\, km/h$$

A projection of the velocity $\mathbf{v}$ in the northerly direction is:

$$v_N = |\mathbf{v}|\sin30\degree = 100\cdot \dfrac{1}{2}= 50\, km/h$$

Answer. $v_E = 70.71\, km/h$, $v_N = 50\, km/h$.