Final answer:
Yes, a variation of 45 degrees in wind direction could be true. To find the wind speed and direction in the scenario given, one must calculate the wind velocity vector components and use them to determine the wind's magnitude and angle.
Step-by-step explanation:
The question you're asking pertains to a scenario where an airplane's heading and velocity are affected by wind. In the given problem, the airplane is heading north at 45.0 m/s, but its actual velocity relative to the ground is 38.0 m/s at an angle to the west of north. To determine the speed and direction of the wind, we need to calculate the difference between the plane's heading and its actual velocity.
To find the wind speed and direction, one can compute the wind velocity vector components and then combine them to get the magnitude and direction. From the problem information, we already have a velocity component of the wind along the y-axis (Vwy), which is -9.29 m/s, indicating motion to the south. This is calculated by multiplying the given velocity relative to the ground by the cosine of the angle from north (38.0 m/s)(0.940) and subtracting the plane's speed (45.0 m/s).
Once the perpendicular components of the wind velocity (Vwx and Vwy) are known, you can use the Pythagorean theorem to find the magnitude of the wind speed, and inverse trigonometric functions such as arctan to determine the direction of the wind expressed in degrees from a reference direction. In this context, a variation of 45 degrees in wind direction is certainly plausible, as wind direction can vary due to a variety of natural factors.