Jose wrote:
What is the net momentum change when the airplane falls to the ground?

The vertical compenent first rises from zero to Vt * M where Vt is the
terminal velocity of the falling aircraft and M is the mass of the
falling
aircraft. Then the vertical component of momentum RAPIDLY drops
to zero again after the aircraft contacts the ground.

Well, actually, only sorta. The momentum of the airplane is equal to
the momentum of the earth, except in sign. Net is zero. The center of
mass of the earth/airplane does not move.

Leave the earth out of it and just look at the aircraft, and you are
correct. And to keep an airplane up, in view of this acceleration, an
opposite acceleration needs to be applied. Air must be thrown down with
sufficient (net) force to counteract gravity's attempt to accelerate the
wing downwards.

No. You can also generate an upward force on an airplane by
creating low pressure over the upper surface of the wing while
the pressure below the wing remains at ambient. I dunno if
there are any airfoils that leave the air below the wing exactly
the same as ambient, but if there were, it would fly. There is
no NEED to throw anything downward.

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FF