The force felt by a pilot when a package is dropped? Here is a physics question that I wish to prove mathematically.
A 100,000 kg aircraft drops a 1000 kg package of supplies over an arctic research station. What approximate force is felt by the 100 kg pilot at the instant of the release?
Is there a reactive force on the plane when the package is dropped?
 A: The floating mechanism that keeps 100000 kg (including plane, load, and pilot), plane afloat, will at the time of release, keep working now on 99000 kg. That means the 99000 kg will feel a 1000 kg upward force/thrust. This force will be also felt by the pilot due to upward thrust of the plane, but it will be negligible. Something like 1/99 m/sec sq. given nothing else is changed.
This is a straight forward estimate without considering any other complex mechanisms which I may not be aware of.
A: Sounds like a homework question. Here is a partial answer. 
Before the drop, gravity acts on the plane, the pilot, and the package. This is the weight of each. After the drop, gravity continues to act on each. The weight of the pilot does not change. 
If the plane is in straight level flight, the upward force of the air on the wings is just enough to counteract the weight of all three. 
If the wings and such stay fixed, the upward force stays the same after the drop. But the downward force is only the weight of the plane plus pilot. 
So think about the total force on the place, and what the acceleration of the plane must be. Since the pilot moves with the plane, he must experience that acceleration. What is the force on the pilot?
A: He'll feel the release of potential energy, which is equivalent to 
$$1000kg*height*gravitational~acceleration$$
The pilot would feel the same effect as if he was dropping an object from his hand weighing 1 kilogram.
