Question

A bear, searching for food wanders 35.0 meters east then 20.0 meters north. Calculate the angle of the bear's displacement (w/respect to his starting position).

Answer 1

Answer:

$29.7^{\circ}$ north of east

Explanation:

Using a reference system in which east corresponds to the x-coordinate and north corresponds to the y-coordinate, the angle of the bear's displacement can be calculated by using the formula:

$tan \theta = \frac{d_y}{d_x}$

where

$d_y = 20.0 m$ is the displacement along the y-direction

$d_x=35.0 m$ is the displacement along the x-direction

Substituting, we find

$tan \theta=\frac{20.0 m}{35.0 m}=0.571\\\theta=tan^{-1}(0.571)=29.7^{\circ}$

where the angle is measured with respect to the x-direction (east).