# A plane is flying with a bearing of 302°. Its speed with respect to the air is 900 kilometers per hour. ?

A plane is flying with a bearing of 302°. Its speed with respect to the air is 900 kilometers per hour. The wind at the plane's altitude is from the southwest at 100 kilometers per hour (see figure). What is the true direction of the plane, and what is its speed with respect to the ground? (Round your answers to two decimal places.)

I got 882.89 km/h for speed (which was correct) but I got 38.31 degrees North of West for direction (which was incorrect). Can anybody help me with direction?

### 1 Answer

- az_lenderLv 71 month agoFavorite Answer
I'm assuming that the "bearing of 302 degrees" is measured clockwise from north. The components of this 900 km/h velocity are 763.24 km/h westward and 476.93 km/h northward.

The components of the wind velocity are 70.71 km/h eastward and 70.71 km/h northward.

The components of the resultant ground velocity are

692.53 km/h westward and 547.64 km/h northward. I agree that the direction is 38.3 north of west, but I got 38.34 degrees rather than 38.31 degrees. Or maybe their beef is that they wanted you to express the direction as a bearing (clockwise from north).