Originally Posted by DakarM
I don't know I think you guys are wayyyyyyyyyyyyyyyyyyyyyyyyyyy over analyzing it.
The read the text as written. The plane will not be moving relative to the ground. Period. That is what it says. It's not a matter of if the plane can generate enough thrust or not to over come the belt.
It states that it will not since the planes speed (the thrust generated by the planes engine) will be matched by the belt.
The problem only states that the conveyor belt moves backward at a velocity equal to the plane's forward velocity, that's it. The thrust from the engines (to first order) is unaffected by the plane's forward velocity: the engine's always push the plane forward.
The question is whether the conveyor belt will provide enough force to cause the plane to counteract the forward thrust from the engines. If it can, the plane won't move, if it can't the plane moves forward. So, think of this. If I hung the plane from the ceiling using string and roll the wheels by hand. This is essentially what the conveyor belt is doing, it is rolling the plane's wheels. So you might get the plane to sway a little bit, but because the wheel can spin freely, your rolling of the plane's wheels does just that, and doesn't move the plane. The other thing this shows is that the RPM the wheels spin has absolutely no bearing on how fast the plane is moving. So, the conveyor belt exerts little to no force on the plane, and the thrust from the engine allows the plane to accelerates forward.