Find the direction of travel as a bearing

Question

In which direction would I have to travel in order to travel East (relative to a stationary observer) if I am flying in a 40kmh^−1 wind coming from the North and can fly at 90kmh^−1 relative to the air? Give your answer as a bearing (degrees clockwise from North) to 3 significant figures.

Answer 1

1. The direction the plane goes is the vector sum of the wind velocity and the plane's velocity.
2. For the plane to go east, the vertical component of the wind's velocity must cancel out with the vertical component of the plane's velocity
3. So v_y for the plane = 40 km/hr north (the wind is heading south)
4. The plane's velocity is the resultant of this v_y and some unknown v_x that must be pointed east to get to the destination.
5. So the plane's bearing must be pointed northeast
6. Draw a right triangle to represent these 3 vectors, with v_y = 40 km/hr and the diagonal with a value of 90 km/hr.
7. Use a² + b² = c² to find the unknown side, v_x
8. Check: This value must be less than 90 km/hr
9. Now we know all 3 sides of this triangle, so we can use trigonometry to find the angle we need for the bearing.
10. Careful: Always reread the question to see how the teacher wants you to express the answer. This one asks for an angle in degrees clockwise from due north, so there will likely be an extra step, depending how you drew your vector triangle.