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.