Question

Two cars, A and B start at the same point. A travels north to 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

$$\vec{v}_{BA}=(8\cos{45},8\sin{45})-(0,-10)\\=(5.66,15.66)\ mph\\v_{BA}=\sqrt{5.66^2+15.66^2}=16.6\ mph\\\theta=\arctan{\frac{5.66}{15.66}}=20\degree\text{ W of S}$$