Question

A plane has an airspeed of 111 km/h. It is flying on a bearing of 79 while there is a 21 km/h wind out of the northeast (bearing 225°). What are the ground speed an the bearing of the plane?

The ground speed is___km/h.
(Round to the nearest tenth as needed.)
The bearing is___°
Round to the nearest tenth as needed.)

Answer 1

To find the ground speed and bearing of the plane, we can use vector addition. The ground speed is approximately 118.9 km/h and the bearing is approximately 72.9°.

Step-by-step explanation:

To find the ground speed and bearing of the plane, we can use vector addition. First, we need to find the components of the plane's airspeed and wind speed in the north and east directions. The airspeed can be split into north and east components using trigonometry. The wind speed can also be split into north and east components using the same method. Then, we can add the north and east components separately to get the resultant ground speed and bearing of the plane.

The north component of the airspeed is found by multiplying the airspeed (111 km/h) by the cosine of the bearing (79°). The east component of the airspeed is found by multiplying the airspeed by the sine of the bearing.

The north component of the wind speed is found by multiplying the wind speed (21 km/h) by the cosine of (225° - 90°). The east component of the wind speed is found by multiplying the wind speed by the sine of (225° - 90°).

Then, we can add the north components and east components together to get the resultant ground speed and bearing of the plane using the Pythagorean theorem and trigonometry.

The ground speed is approximately 118.9 km/h and the bearing is approximately 72.9°.