Question

An airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the plane, is from the southwest and has a velocity of 60 miles per hour. What is the true direction of the plane, and what is its speed woth respect to the ground?

I have no idea where to start!

Answer 1

Thank you!!

Answer 2

North speed = v
East speed = u

Wind u = 60 cos 45 = 42.4
Wind v = 60 sin 45 = 42.4

plane u = -580 sin 60 = -502
plane v = +580 cos 60 = +290

total u = 42.4 - 502
total v = 42.4 + 290

now do sqrt (u^2 + v^2)
and tan^-1 (v/u)