Final answer:
Using the Pythagorean theorem, the magnitude of the plane's displacement is found to be approximately 561 km. However, this answer is not exactly reflected in the given choices, suggesting there could be a misprint.
Step-by-step explanation:
To find the magnitude of the plane's displacement from its starting point after flying 360 km east and then 430 km north, we can use the Pythagorean theorem. This is a right-angled triangle problem where the distances east and north represent the perpendicular sides of the triangle, and the displacement is the hypotenuse.
Let's denote the displacement as D, the eastward distance as A (360 km), and the northward distance as B (430 km).
- D = √(A² + B²)
- D = √(360² + 430²)
- D = √(129600 + 184900)
- D = √(314500)
- D ≈ 561 km (rounded to the nearest kilometer)
However, none of the options closely match the computed displacement. Therefore, it is possible there might be a mistake in the given answer choices or in the question itself. In practice, the student should double-check the question and then select the closest answer or seek clarification.