Airplane Velocity Calculation

What are the velocities involved in the airplane travel scenario?

1) The velocity of the plane with respect to the air is 120 m/s due east.

2) The velocity of the air with respect to the ground is 43 m/s at an angle of 30° west of due north.

Answers:

1) What is the speed of the plane with respect to the ground?

2) What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).

3) How far east will the plane travel in 1 hour?

In the scenario provided, the speed of the plane with respect to the ground can be calculated by using vector addition. The first step is to break down the velocity of the plane with respect to the air into its horizontal and vertical components.

Using the given information:

Velocity of plane with respect to air (VPA) = 120 m/s due east

Velocity of air with respect to ground (VAG) = 43 m/s at 30° west of due north

1) To find the speed of the plane with respect to the ground, we need to consider the vector addition of VPA and VAG. This can be done by using the law of cosines:

VPG = sqrt[(120)^2 + (43)^2 - 2(120)(43)cos(150°)]

2) To determine the heading of the plane with respect to the ground, we can calculate the angle using the law of sines:

tan(θ) = (120sin(90° - 30°)) / (120cos(90° - 30°) + 43)

Heading = 90° - θ

3) The distance traveled east by the plane in 1 hour can be calculated by multiplying the speed of the plane with respect to the ground by the time taken, which is 1 hour.

Distance east = Speed of plane with respect to ground * Time

By following these calculations, we can determine the speed of the plane with respect to the ground, its heading, and the distance it travels east in the given scenario.