Question

In midtown Monrovia, the street blocks have a uniform size of 80 m x 280 m, with the shortest side oriented at 29 east of north (“uptown”) and the long side oriented at 29 north of west. Suppose you walk three blocks uptown and then two blocks to the left. What is the magnitude and direction of your displacement vector?

Answer 1

$$s=3(80\sin{29},80\cos{29})\\+2(-280\cos{29},280\sin{29})=(-373.4,481.4)\ m$$

$$s=\sqrt{373.4^2+481.4^2}=609\ m$$

$$\theta=\arctan{\frac{373.4}{481.4}}=37.8\degree\text{W of N}$$