Final answer:
The student's question is about using vector subtraction to calculate the speed and direction of the wind affecting an airplane's travel. The approach involves drawing a vector triangle and employing the Pythagorean theorem and trigonometry to solve for the unknown wind vector, thus determining its impact on the plane's ground speed.
Step-by-step explanation:
The student's question involves calculating the speed and direction of the wind affecting an airplane's relative ground speed. In this scenario, the plane is heading north at 45.0 m/s, but its ground speed is only 38.0 m/s in a direction west of north. To determine the wind's effect on the plane, we can use vector subtraction.
The wind's speed and direction are the vectors needed to be added to the plane's airspeed to result in the ground speed vector.
By drawing a vector triangle with the plane's northward velocity and westward ground velocity, we can use Pythagorean theorem and trigonometry to calculate the wind's velocity vector. Since the ground speed is less than the airspeed, the wind is acting opposite the plane's direction of travel (west of north), slowing it down and pushing it westward.
The calculated wind velocity for a similar problem resulted in a speed of 230 m/s at an angle of 8.0° south of west, indicating that the wind's direction can be expressed as an angle from a cardinal direction, and it influences both the magnitude and direction of the plane's ground speed.