Question

A boy walks to the store using the following path: $0.4$ miles west, $0.2$ miles north, $0.3$ miles east. What is the direction of the vector that points from his house directly to the store? (in degrees)

• A. $63.4$
  
• B. $64$
  
• C. $63$
  
• D. $65$
  

Answer 1

The correct option is A $63.4$

Consider east direction to be x-axis and north direction to be y axis.
Total displacement along x axis $S_x=-0.4\hat{i}+0.3\hat{i}=-0.1\hat{i}$
Displacement along y axis $S_y=0.2\hat{y}$
Direction of net displacement from x-axis $\tan \theta =\frac{S_y}{S_x}=\frac{0.2}{0.1}=2$
$⟹\theta =\tan \left(2\right)={63.4}^o$