Question

An airplane pilot sets a compass course due west and maintains an airspeed of 214 km/hkm/h. After flying for a time of 0.480 hh, she finds herself over a town a distance 124 kmkm west and a distance 13 kmkm south of her starting point.

Answer 1

The question involves vector components, displacement, and navigating an airplane in the presence of a crosswind, which are key concepts in physics specifically related to kinematics and dynamics.

Step-by-step explanation:

This question is addressing the concepts of vectors and their components, as well as the effect of external forces such as wind on the displacement of an object—in this case, an airplane. Specifically, we are looking at breaking down a displacement vector into its south and west components in the first part (a) and then into components along a set of axes rotated 45° in the second part (b). Moreover, the question involves calculating the resultant displacement and direction when the airplane takes two consecutive paths at different angles. Then, it addresses how the flight path is affected by wind coming from certain directions and how to adjust the course to counteract this wind.

In the example provided, we also explore how the pilot must alter the plane's heading to maintain a desired direction in the presence of a crosswind, which is a common real-world aviation challenge.