Final answer:
To find the speed and direction of the air currents, we can use vector addition, drawing a diagram to visualize the vectors and applying trigonometry. The airspeed and ground speed are vectors, and by comparing the given information with the resultant ground speed, we can calculate the speed and direction of the wind.
Step-by-step explanation:
We are given that a plane has an airspeed of 200 miles per hour and a heading of 22.0°. The plane's ground speed is 228 miles per hour, and its true course is 40.0°. To find the speed and direction of the air currents, we can use vector addition, where the airspeed and its direction represent one vector and the wind speed and direction represent the second vector. The ground speed and direction are the resultants of these two vectors.
To solve the problem, we would typically draw a vector diagram to visualize the vectors and then apply trigonometry to calculate the magnitude and direction of the wind. However, as this is a textual response, I will describe the process:
- Draw a vector representing the plane's airspeed and direction.
- Draw a vector representing the ground speed and direction as the resultant.
- Use the known angles and the law of sines or cosines to determine the magnitude and direction of the wind vector, ensuring the direction is measured relative to north.
This calculation is an example of vector decomposition into its components, one of which is known (airspeed and heading of the plane), and the other (wind speed and direction) is what we are trying to find.