Question

A plane has an airspeed of 130 km/h . it is flying on a bearing of 84 while there is a 27 km/h wind out of the northeast​ (bearing 225​). what are the ground speed and the bearing of the​ plane?

Answer 1

The ground speed of the plane is approximately 132.15 km/h and the bearing of the plane is approximately 83.38°.

Step-by-step explanation:

To find the ground speed and bearing of the plane, we can use vector addition. The airspeed of the plane is 130 km/h at a bearing of 84°. The wind is blowing at 27 km/h from the northeast, which has a bearing of 225°.

1. First, we need to resolve the airspeed and wind speed into their east-west (x) and north-south (y) components.
2. Next, we add the x-components and the y-components separately to find the total x and y components.
3. Finally, we use the Pythagorean theorem and trigonometry to find the magnitude and direction of the resultant vector (ground speed and bearing).

Using this method, we can determine that the ground speed of the plane is approximately 132.15 km/h and the bearing of the plane is approximately 83.38°.