A delivery drone generates an airspeed of 12 m s⁻¹ when it points its nose due north relative to the air. A steady wind blows at 5.0 m s⁻¹ toward 40° south of east.
The drone must deliver a package to a location that lies 500 m due north of the launch point at the lowest possible flight time.
(a) When the drone maintains its nose due north, determine its velocity relative to the ground (magnitude and compass direction).
(b) With the orientation from part (a), calculate how far east or west of the target the drone will be when it has traveled the required 500 m northward component.
(c) To arrive exactly at the target, determine the heading (direction the nose must point) the pilot should set and compute the resulting flight time.
(d) Qualitatively explain how both the required heading and the flight time would change if the wind speed were to double while its direction remained the same.