Question

A person walks 46 m East and then walks 39 m at an angle of 47 degrees North of East. What is the magnitude of the total dis-placement ? Answer in units of m.

Answer 1

Let's assume that person starts at point A, after walking 46m East he/she changes the direction at point B and then stops walking and point C. We have triangular ABC with AB=46m, BC=39m, $\angle B= 47^\circ$ .The total displacement is the side of triangular AC. To find it we can use cosine theorem:

$AC^2 = AB^2 + BC^2 - 2 AB \cdot BC \cdot cos47^\circ$

$AC^2 = 3637- 2447=1190$

$AC = \sqrt{1190}=34.5$ m.

Answer: 34.5 m