Calculating Airplane Speed and Heading
Explanation:
The given scenario involves an airplane traveling 30° south of due west at 180 m/s with respect to the air, while the air is moving with a speed of 31 m/s with respect to the ground due north. To solve the questions posed, we utilize vector addition and trigonometry to determine the speed and heading of the plane with respect to the ground.
1) Speed of the plane with respect to the ground: By combining the velocities of the plane with respect to the air and the air with respect to the ground using the Pythagorean theorem, we find that the speed of the plane with respect to the ground is approximately 183 m/s.
2) Heading of the plane with respect to the ground: Using trigonometry, we calculate the direction of the resultant velocity relative to due north to determine that the heading of the plane with respect to the ground is approximately 240°.
3) Distance traveled east in 1 hour: To find out how far east the plane will travel in 1 hour, we multiply the speed of the plane with respect to the ground by the time taken to arrive at approximately 659.4 km.
By understanding the principles of vector addition and trigonometry, we can accurately determine the speed, heading, and distance traveled by the airplane in this scenario.