Question

Margaret walks to the store using the following path: 0.740 miles west, 0.300 miles north, 0.240 miles east. Assume north to be along the +y-axis and west to be along the -x-axis

whats the direction of displacement vector

Answer 1

Given:

${\vec d_1}=-0.740\hat i$

${\vec d_2}=0.300\hat j$

${\vec d_3}=0.240\hat i$

The displacement

$${\vec d}={\vec d_1}+{\vec d_2}+{\vec d_3}$$

So

$${\vec d}=-0.740\hat i+0.300\hat j+0.240\hat i\\ =-0.500\hat i+0.300\hat j$$

The direction of displacement is

$$\theta=\tan^{-1}\frac{d_y}{d_x}=\tan^{-1}\frac{0.300}{-0.500}=149^{\circ}$$

from positive $x$ direction or $31^{\circ}\: \rm N\: of\: W$.