After release the payload moves under gravity and quadratic air drag: m dv/dt = m g − ½ ρ (Cd A) |v − w| (v − w), with w the wind velocity. The box has Cd A = 0.063 m2; a parachute adds Cd = 1.5 times its canopy area, opening over 0.5 s after the chosen delay. The trajectory is integrated with fourth-order Runge-Kutta (10 ms step, interpolated landing).

Without drag the lead distance is the textbook x = v √(2h/g); the dashed curve is that vacuum case. With drag the payload decelerates horizontally and its vertical speed tends to the terminal value vt = √(2 m g / (ρ Cd A)). A tailwind carries the payload further, so the lead grows; a headwind shortens it. The release offset slider moves the drop zone to show what a mistimed release costs in metres.

Simplifications: constant air density, parachute opens instantly (with a short ramp) without a shock load or swing, 2D motion. Educational physics for relief logistics, not flight planning.