A pilot is flying a Cessna airplane at 180 mph (airspeed).He would like to fly in the direction N45W, but there is a 32 mph wind in the S60W direction.What direction should the pilot set his course for in order to fly along his desired track? What will his speed relative to the ground be?

Answer 1

Draw a diagram of the velocities. If the plane's heading is θ, we need the final x- and y-components to be N45W. So,

180sinθ - 32cos60 = v sin135
180cosθ - 32sin60 = v cos135

θ = 20°
v^2 = 180^2+32^2-2*180*32 cos40°
v = 157 mph