Final answer:
The plane's total displacement after flying 150 km north and 400 km east is approximately 427.3 kilometers in a direction of about 20.56° north of east.
Step-by-step explanation:
The plane's total displacement after flying 150 km north and 400 km east can be determined using the Pythagorean Theorem. Consider the movement as a right-angled triangle where the legs are the north and east components of the journey. To find the hypotenuse, which represents the displacement, we calculate the square root of the sum of the squares of these two legs.
Displacement = √(150 km)² + (400 km)²
= √(22500 km² + 160000 km²)
= √182500 km²
= 427.3 km
The direction of the displacement can be found using trigonometry, particularly the tangent function, as the angle of displacement, θ, will be tan⁻¹(150/400).
θ = tan⁻¹(150/400)
θ = tan⁻¹(0.375)
θ ≈ 20.56°
Thus, the plane's total displacement is approximately 427.3 km in a direction ≈ 20.56° north of east.