Answer
The path of the falling object will be a parabola as seen by a ground-based observer (page 185).
In your reference frame on the plane, with no air resistance, the object falls straight down along a vertical path.
It lands directly beneath you, from your perspective.
In the more realistic case where we do not neglect the effects of air resistance on the care package, air resistance reduces its forward-directed horizontal component of velocity. We predict it will land behind the airplane.
