Calculate Ground Speed and Direction of an Airplane

What is the ground speed and direction of an airplane?

An airplane is traveling due north at 130km/hr with a mild crosswind heading due east at 30km/hr.

Ground Speed and Direction Calculation

To calculate the ground speed of an airplane affected by a crosswind, use the Pythagorean theorem to find the magnitude of the resultant vector, and the inverse tangent function to determine the direction angle.

When an airplane is flying north at 130km/hr with a crosswind blowing east at 30km/hr, we can calculate the ground speed and direction using vector addition techniques.

The ground speed can be found by using the Pythagorean theorem to calculate the magnitude of the resultant vector. In this case:

Ground Speed = √((130km/hr)^2 + (30km/hr)^2)

For the direction, we would use the inverse tangent function (arctan) to find the angle of the resultant vector with respect to due north. The calculation would be:

Direction = arctan(30/130)

The ground speed is the hypotenuse of the right-angled triangle formed by the velocities, and the direction would be east of north at the calculated angle. This method allows us to determine the airplane's actual speed and heading in relation to the ground.