Final answer:
The total distance traveled is 900 km and the total displacement is 640 km at a direction of 53.1 degrees north of east.
Step-by-step explanation:
To find the total distance traveled by the airplane, we add up the distances traveled in each leg of the journey.
The airplane travels 300 km to the north, then 400 km to the east, and finally 200 km to the north again.
Adding these distances, the total distance traveled is 300 km + 400 km + 200 km = 900 km.
To find the total displacement of the airplane, we need to consider the magnitude and direction of each leg of the journey.
The north direction is represented by a positive value, while the east direction is represented by a negative value.
The total displacement is the vector sum of these individual displacements.
The north displacement is 300 km + 200 km = 500 km north, and the east displacement is 400 km east.
Using the Pythagorean theorem, the magnitude of the displacement is found to be √(400^2 + (500)^2)= 640 km.
The direction of the displacement can be found using the tangent function, tan θ = opposite/adjacent, where θ is the angle between the displacement vector and the positive x-axis. tan θ = 500/400, so θ = 53.1 degrees north of east.