A hiker begins a trip by first walking 25.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 40.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger’s tower. (a) Determine the components of the hiker’s displacement for each day. (b) Determine the magnitude and direction of the total displacement.

(a)

(b)

Explanation:

Let us take the north direction to be the positive y-axis and the east to be positive x-axis.

First day:

25.0 km southeast, which implies south of east. The y-component will be negative and the x-component will be positive.

Second day:

She starts off at the stopping point of last day. This time, both the y- and x-components are positive.

Therefore, total displacements:

Magnitude of displacements,

Direction,