How to pick a load from the ground to a flying airplane? The following system was used by the US military, Navy and CIA since WW II.
The load is attached to one end of the rope, and a baloon to another end. The baloon stretches the rope vertically. An airplane flies horizontallty at a constant speed, heading at the rope. A special clamp in the front end of the airplane catches the rope, and at the same time cuts off the upper portion of the rope with the baloon.
The load is lifted and then it is slowly moved to the airplane with a winch.
A surprising thing is that the load begins its motion almost vertically, it is not dragged on the surface. Another feature is that the acceleration experienced by the load is not very large. All this makes possible to lift non only dead loads but also people from arbitrarily rough terrain (like ice, rocks etc.) and from the sea surface. Some people think that the crucial thing is elasticity of the rope (or of the clamping device in the airplane). This is not so.

Problem. In the idealized model when the rope does not stretch at all, find the approximate trajectory of the lifted object, and compute the acceleration in the beginning of the lift. Make some reasonable assumptions about the length of the rope and the speed of the airplane.