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

`29.7^(\circ)` north of east

Step-by-step 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 = (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=(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).