After equilibrium
occurs the fan no longer puts any net momentum into the air
mass. The momenta of the individual air molecules cancel.

Yes, but only because of the wall, which allows the pressure to build up
on the far side of the fan. Were there no wall (such as for an airplane
propeller), this would not be the case.

The collison with the dribbler is inelastic. Energy is conserved,
momentum is not.

Well, only if you treat momentum as a scalar, or deal only with the
momentum of a single particle at a time. If two glueballs collide, (for
simplicity assume they were of equal mass, equal and opposite velocity),
the net (vector) momentum before is zero, but each glueball will have a
finite momentum because it is moving. After the collision, the net
(vector) momentum is zero (the splatball is motionless), and each
glueball component of the splatball is also motionless. The glueballs
have each lost momentum, because they have stopped.

So, while the vector sum of the momenta have not changed, the (scalar)
sum of the absolute values of the momenta have.

Kinetic energy (mv^2/2) is =not= conserved in an inelastic collision,
since v changes, and v^2 is scalar. It is transformed into other forms.
Some of that kinetic energy becomes heat and noise (which is
ultimately molecular kinetic energy), some of it shakes electrons
around, but macroscopic kinetic energy is not conserved for an inelastic
collision.

He uses energy to impart momentum to the basketball

So, he is "throwing basketballs down". They could just as easily be
very very tiny basketballs; the kind with eight electrons or so.

Precisely. He does not need the earth beneath him any more than
an airplane wing needs the Earth beneath it.

No, he doesn't need the earth in order to =stay=up=. But the system
=does= need the earth to satisfy the "no net momentum change in the
basketballs/air" criterion. Absent the earth's surface, there =is= a
net momentum change, whether the basketballs are the size of
basketballs, or the size of air molecules.

Jose
--
Money: what you need when you run out of brains.
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