1. Visualize the Problem

Imagine a coordinate plane. The duck's movement can be represented as two sides of a right triangle:

* East (x-axis): 2.5 meters

* North (y-axis): 6.0 meters

2. Find the Hypotenuse

The displacement is the hypotenuse of this right triangle. We can use the Pythagorean theorem to find it:

* a² + b² = c²

* (2.5 m)² + (6.0 m)² = c²

* 6.25 m² + 36 m² = c²

* 42.25 m² = c²

* c = √42.25 m²

* c ≈ 6.5 m

3. Determine the Direction

We'll use the arctangent function (tan⁻¹) to find the angle (θ) of the displacement with respect to the horizontal (east):

* tan θ = (opposite side) / (adjacent side)

* tan θ = 6.0 m / 2.5 m

* θ = tan⁻¹ (6.0/2.5)

* θ ≈ 67.4°

Answer

The magnitude of the duck's displacement is approximately 6.5 meters, and the direction is approximately 67.4° north of east.