Speed and Heading of an Airplane with Respect to the Ground
What is the speed of the plane with respect to the ground? ______ m/s
1) 157.5 m/s
What is the heading of the plane with respect to the ground? (Let o* represent due north, 90 represents due east). _____ East of due North
2) 30° east of due north
How far east will the plane travel in 1 hour? ______ m
3) 157.5 km
Final answer:
The speed of the plane with respect to the ground is 157.5 m/s. The heading of the plane with respect to the ground is 30° east of due north. The plane will travel 157.5 km east in 1 hour.
Explanation:
To find the speed of the plane with respect to the ground, we can use vector addition. The velocity of the plane with respect to the ground can be found by adding the velocity of the plane with respect to the air to the velocity of the air with respect to the ground. Using the given values, the speed of the plane with respect to the ground is √(150^2 + 39^2 - 2 * 150 * 39 * cos(30)) m/s, which is approximately 157.5 m/s.
To find the heading of the plane with respect to the ground, we can use the angle of the air velocity. The heading will be the angle between the resultant velocity and the north direction. Using the given values, the heading of the plane with respect to the ground is 30° east of due north.
To find how far east the plane will travel in 1 hour, we can multiply the speed of the plane with respect to the ground by the time. Using the given speed of the plane with respect to the ground, the plane will travel 157.5 km east in 1 hour.