Final answer:
To calculate the displacement, the horizontal and vertical components for each part of the plane's journey must be summed, and then the Pythagorean theorem is applied to these sums to find the total displacement.
Step-by-step explanation:
The student's question involves calculating the total displacement of a plane after two legs of travel at different angles. To solve this, it's crucial to break down the displacement into its horizontal and vertical components for each leg. For the first leg at 45°, the horizontal and vertical displacements are equal, due to the angle's inherent properties in a right-angled triangle. This means we have 2.5km in the horizontal direction and 2.5km in the vertical.
After changing its angle to 25° for the second leg of 5.2km, we again calculate the horizontal and vertical components, which involve some trigonometric calculations. The final step is to sum the horizontal components and the vertical components separately and then use the Pythagorean theorem to find the overall displacement.