One problem: Remember that projector on a cart and the iPad 2 plugged in with a cable? Yeah, a lot of moving objects fly around a school gym filled with 3-5th graders. As you can imagine, classroom management is fairly difficult with a 4' cord tethering you and your iPad to a corner of the gym.
Solution: Sure, you can buy projectors that mount on the ceiling, or that are powerful enough to go from one side of the gym to another, but the cost of specialized projectors and mounting lead us to a different approach...
Locally-fabricated projector cage made out of metal and carbon fiber
An ultra short-throw projector with an Apple TV taped next to it.
The wooden tray next to the projector is an old existing sound system they tied the Apple TV into.
(Technicians and custodians involved in the installation chose the first YouTube video)