Final answer:
The student's question involves vector addition to determine the resulting speed and direction of an airplane's ground speed when affected by wind. The problem involves calculating the plane's ground speed using its airspeed and wind's velocity, accounting for both crosswind and head-wind components.
Step-by-step explanation:
The question is dealing with a physics concept known as vector addition, where the velocity of the plane and the velocity of the wind combine to give a resulting ground speed for the airplane. To find the resulting speed of the plane as it is affected by wind, we utilize vector addition to combine the plane's airspeed with the wind's speed and direction. For example, if an airplane is heading north at 45.0 m/s (its airspeed) and is subjected to wind with a velocity such that the plane's ground speed is 38.0 m/s at an angle west of north, we can infer that there is a significant crosswind component as well as a head-wind component affecting the plane's trajectory.
From Figure 3.44, it's apparent that the wind is blowing in such a manner that it slows down the airplane and pushes it westward, resulting in a total velocity that is both slower and at a different angle than the airplane's intended northern direction. Additionally, through calculations or examples provided like in Figure 3.48 and example 4.14, we can determine the speed and direction of the wind affecting the plane. Considering these factors, the airplane's ground speed is the result of vectorially adding the plane's velocity and the wind's velocity. This is a critical task for a pilot, especially when navigating to ensure that the desired course and destination are maintained.