A dog searching for a bone walks 3.5 m south, then 8.2 m at an angle of 30.° north of east, and finally 15 m west. What was the dog's resultant displacement.

First, we resolve the diagonal movement in to components of north and east.

north = 8.2sin (30)

north = 4.1 m

east = 8.2cos (30)

east = 7.1

Vertical movement: 4.1 - 3.5 = 0.6 m north

Horizontal movement: 15 - 7.1 = 7.9 m west

Magnitude = √ (0.6² + 7.9²)

Magnitude = 7.92 m

Direction:

tan∅ = y/x

tan∅ = 0.6 / 7.92

∅ = 4.33°

The dog walks 7.92 meters at an angle of 4.33° from south