Vectors and velocity

Question

A plane heads at an angle of 30 degrees west of north at a speed of 250m/s. Calculate the westward and northward components of the planes velocity

Answer 1

Velocity of the plane is represented with vector $\vec{AC}$ and the magnitude of that vector is $AC=250\frac ms$. On the other side $\vec{AC}=\vec{AB}+\vec{BC}$, with $\vec{AB}$ representing the northward and $\vec{BC}$ representing the westward component of velocity.

You can easily calculate magnitudes of these two components if you notice that $\triangle ABC$ is actually a half of the equilateral triangle $\triangle ADC$:

$$BC=\frac12 AC=\frac12 \cdot 250 \frac ms = 125\frac ms$$

$$AB=\frac{\sqrt{3}}{2} AC=\frac{\sqrt{3}}{2} \cdot 250 \frac ms = 125\sqrt3\frac ms\approx 216.5\frac ms$$