Question

Two cars, A and B, start at the same point. A travels north at 10 mph and B at 8 mph due

southwest. Find in what direction and rate by which car B is moving, with regards to car A. 

Answer 1

$$\bf V_{BA}=V_B-V_A$$

$$V_{BAx}=-8\cos45^\circ-0=-5.7\:\rm mph$$

$$V_{BAy}=-8\sin45^\circ-10=-15.7\:\rm mph$$

The magnitude of relative velocity

$$V_{BA}=\sqrt{5.7^2+15.7^2}=16.7\:\rm mph$$

Direction

$$\theta=\tan^{-1}\frac{-15.7}{-5.7}=70^\circ \quad \rm S\: of\: W$$