Final answer:
The student's task involves calculating the resultant displacement for a plane journey that comprises two legs at right angles to each other. By using the Pythagorean theorem to determine the magnitude and trigonometry to find the direction, the resultant displacement is approximately 338 km at 34.16° from north of east.
Step-by-step explanation:
The student is asked to work with displacement and resultant vectors in two scenarios: first, an airplane traveling between airports with specified directions and distances, and second, breaking down this displacement into components along different axes. In the first scenario, the plane travels 280 km east and then 190 km north. To sketch the displacement, one would draw an eastward horizontal line (for the first leg of the journey) and then at the endpoint of that line, draw a vertical line upward (for the northward leg of the journey).
The resultant displacement is the straight line from the starting point to the final position (Airport C), which can be found using the Pythagorean theorem. This is a right-angled triangle with the eastward travel as one leg and the northward travel as the other leg. The magnitude of the resultant displacement can be calculated as √(2802 + 1902) km, which gives approximately 338 km. The direction of the displacement can be determined using trigonometry, specifically the arctan function, to find the angle that the resultant displacement makes with the eastward direction, which comes out to about 34.16° from north of east.