A plane is headed due west with an air speed of 215 m/s. The wind blows south at 20.0 m/s. Find the velocity of the plane relative to the earth.

Question

Find the velocity of the plane relative to the earth.

magnitude: 215 m/s

direction:  ? degrees south of west

how do i find the direction

Answer 1

Here is a sketch:

Can you see that the trig ratio "tangent" relates the angle θ with the opposite side "20" and the adjacent side "215"?

tan(θ) = opp/adj = 20/215

so θ = tan^-1(20/215)

Use the "tan^-1" button on your calculator. Make sure you are in "degree mode". The answer is close to 5° south of west

By the way, your calculation of the magnitude isn't quite right. Should be 216 m/s