Your dog is running around the grass in your backyard. He undergoes successive displacements, 3.60 m south, 8.46 m northeast, and 15.6 m west. What is the resultant displacement? (take + x direction to be east). Find magnitud? Find direction?

First, we resolve the northeast displacement into its north and east components. The angle from the positive x-axis of a northeast displacement is 45 degrees. Thus:

North = 8.46sin (45) = 5.98 m

East = 8.46cos (45) = 5.98 m

North displacement = 5.98 - 3.6 = 2.38 m

West displacement = 15.6 - 5.98 = 9.62

Magnitude = √ (2.38² + 9.62²)

Magnitude = 9.91 m

Direction:

tan∅ = 2.38 / 9.62

∅ = 13.9° north from east