Question

A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement using the component method.

Answer 1

The displacement

$${\bf d}={\bf d_1}+{\bf d_2}+{\bf d_3}$$ $$d_x=d_{\rm East}=0+(-2.20)+0=-2.20\:\rm km$$ $$d_y=d_{\rm North}=3.25+0+(-1.50)=1.75\:\rm km$$

Magnitude:

$$d=\sqrt{d_x^2+d_y^2}=\sqrt{(-2.20)^2+1.75^2}=2.81\:\rm km$$

Direction:

$$\theta=\tan^{-1}\frac{d_y}{d_x}=\tan^{-1}\frac{1.75}{-2.20}=38.5^{\circ}\; \rm N\;of\;W$$