1. The problem statement, all variables and given/known data An airplane wishes to fly from A to B which is located 1000 km northeast of A. The maximum speed of the plane in still air is 650 km/hr. There is a wind blowing West of 40 km/hr In what direction should the pilot steer the plane to complete the trip as fast as possible? 2. Relevant equations 3. The attempt at a solution I drew a diagram where an arrow from origin is 45 degrees above the east axis. Then at the head of that arrow is the head of the west arrow pointing west. and the two tails are connected for the plane's direction with the unknown angle between the plane velocity and the east axis. velocity of plane in still air (vp)= 650(cos θ, sin θ) velocity of wind (vw)= (-40, 0) total velocity = |vtot| (cos 45, sin 45) = vp + vw where |vtot| is the magnitude of the total velocity Computing x component gives me: |vtot| cos 45 = 650cosθ - 40 Computing y component give me: |vtot|sin45 = 650sinθ I've isolated for |vtot| but i don't know what to do after that.