Final answer:
The student's question about the plane's northward displacement after a turn can be solved using trigonometry by calculating the northward component of the displacement vector through the cosine of 30° multiplied by the total displacement of 200 mi.
Step-by-step explanation:
The question asks how much farther north a plane ends up from where it started its turn after flying 200 mi in a direction of 30° north of east. This problem can be solved using trigonometry, specifically by finding the northward component of the plane's displacement vector.
To find the northward displacement (the distance the plane traveled north), we can use the cosine function, which is applied to the angle between the direction of displacement and the northward direction. Since the angle given is north of east, the angle we need for the cosine function is also 30°. The formula to calculate the northward displacement is:
Northward displacement = Total displacement × cos(angle)
In this case, it is:
Northward displacement = 200 mi × cos(30°)
After performing the calculation, we determine how far north the plane has traveled from the point where it started its turn.