A duck waddles 2.5 m east and 6.0 m north. what are the magnitude and direction of the duck's displacement with respect to its original position?

Define the displacement of the duck in a rectangular (x, y) coordinate system.

Refer to the figure below.

The starting position is (0,0).

The first travel takes the duck to (2.5, 0).

The second travel takes the duck to (2.5, 6)

The magnitude of the final displacement is

d = √[6² + 2.5²] = √42.25 = 6.5 m

The angle that the final position makes with the x-axis is

θ = tan⁻¹ (6/2.5) = tan⁻¹ 2.4 = 67.4°

Answer:

The final position is

6.5 m from the original position,

67.4° from the x-axis, measured counterclockwise.