Until the prop generates enough thrust to spin the wheels at the same speed as the conveyer, it's not doing much of anything to change the airflow over the wings, but if it took much thrust to spin the wheels every plane would tip up on its nose at every landing. The wheels must spin freely with little tangential force required.

Once the wheels are spinning fast enough, the airplane can begin to move forward and take off normally. The additional thrust to take off once the wheels are up to speed should be quite comparable to the thrust required for a normal takeoff.

The problem is inadequately stated for a complete analysis, since the width of the belt is not given (and I haven't seen the movie) but there is a "component" in the problem that could have an effect in the form of "boundary layer behavior." When an object (a surface) moves in a fluid (in this case air) the fluid immediately at the surface moves at the same speed as the surface, so the conveyer belt is effectively an air pump, dragging a layer of air with it. The absolute velocity in a fluid cannot change abruptly, so additional air is dragged along with decreasing speed as one moves farther from the surface. As the speed of the moving surface increases, the "boundary layer" becomes a little thicker.

There are a few airplanes that can "fly" in relative air near or slightly below the 50 mph specified, so that if the conveyer is wide enough (possibly near normal landing strip width?), it would be possible for an airplane of this kind to "fly" (lift its weight entirely off the conveyer) without having forward absolute speed. Once the plane is "off the belt" it could accelerate and take off normally.

Unfortunately the boundary layer is not very thick for relative speeds in the range given, so if the plane tries to ascend more than a little above the belt it will rapidly move into air with lower absolute velocity, and likely will perform the four standard maneuvers** every pilot knows well.

The same fluid behavior is what's well known to pilots as "ground effect." At altitude, with lots of air surrounding, the plane drags a lot of air along with it, and must have enough speed so that the net relative wind is sufficient to lift it. When approaching the ground, the air is "bound" to the ground, so at the same forward speed there is less air moving along with the plane, and lift is enhanced enough that the actual stall speed may drop to lower levels than when in flight. This is the effect that sometimes causes amateur pilots to "float a landing" and touch down much farther down the runway than they expect (or go past the end of the runway and do those famous four maneuvers again). If the plane has slowed below free air stall speed but is still above stall in ground effect, attempting to pull up before getting enough speed to be above free-air stall will inevitable produce all four maneuvers. Going up always reduces speed, and a significantly higher speed is required as one moves out of the ground effect.***

** While nearly all here will already know the four standard maneuvers, for the benefit of the few who might not, they are (always performed in the same order) STALL - SPIN - CRASH - BURN. Every pilot must know them before being allowed to take the controls.

*** There might be a few more who might not know that rate of climb - whether you go up or down - is something you control with the throttle in an airplane. Airspeed - how fast you go - is what's changed when you move the stick (or "steering wheel" in the fancy ones). The other bit of info is that you control which direction you're going with the pedals on the floor. "Turning the wheel" - or moving the stick sideways - changes the direction you're pointing, but failure to use the pedals properly will demonstrate that most airplanes can fly sideways quite nicely - within limits.

John