For me, there are two incompatible notions here.
1. the thrust from the jets act on the air, they don't care whether there are wheels, ice, or even if the plane is superglued to the floor!
2. The conveyor does not drive the plane backwards and is designed in the question to represent what would happen if you were to walk or cycle at speed x, the treadmill would match that and you would stay stationary.
With problems like this, it's best to examine the extremes, so the moment the jet engines kicked in... from zero km/h to 0.00001 km/h the treadmill would turn and (if in the ideal scenario, could instantly match the planes speed) the plane would be stationary.
However, the engines are still thrusting us forward, so the plane would again move forward, but this time from 0.00001 km/h to 0.00002 km/h, and the treadmill will instantly match that, and we'd be stationary.
This then is repeated until the wheels and treadmill reach an infinite speed... so no take off.
This is how I imagined the questioner structured the original question.
1. the thrust from the jets act on the air, they don't care whether there are wheels, ice, or even if the plane is superglued to the floor!
2. The conveyor does not drive the plane backwards and is designed in the question to represent what would happen if you were to walk or cycle at speed x, the treadmill would match that and you would stay stationary.
With problems like this, it's best to examine the extremes, so the moment the jet engines kicked in... from zero km/h to 0.00001 km/h the treadmill would turn and (if in the ideal scenario, could instantly match the planes speed) the plane would be stationary.
However, the engines are still thrusting us forward, so the plane would again move forward, but this time from 0.00001 km/h to 0.00002 km/h, and the treadmill will instantly match that, and we'd be stationary.
This then is repeated until the wheels and treadmill reach an infinite speed... so no take off.
This is how I imagined the questioner structured the original question.
