An ambitious hiker walks 25 km west and then 35 km south in a day. find the magnitude and direction of the hikers resultant displacement (relative to due west).

Refer to the diagram shown below.

The resultant displacement, d, is the vector sum of distances traveled west and south.

The magnitude of d is

d = √ (25² + 35²) = 43.012 km

The angle that d makes below due west (or south of west) s

θ = tan⁻¹ (35/25) = 54.5°

Answer:

The resultant displacement is 43.0 km, at an angle of 54.5° south relative to due west.