So this questions had made it rounds before, however, my professor at my flight school still has the wrong answer. what do you guys think the correct answer is?

But nobody is breaking the question except for you by saying the conveyor would somehow be independent of the jet accelerating. We HAVE to assume the conveyor speeds up with the wheels. So the ONLY way for the question to remain intact is to have the wheels and conveyor spin faster than the airplane's forward motion.

Lets say I have a stationary airplane sitting on a treadmill being held in place somehow. Just like your roller blade analogy. Now lets imagine that the treadmill starts moving up to 10mph or something. This in turn causes the wheels to spin at 10mph. But, the airplane is still stationary.

Now, lets turn on the engine on our plane, just like you pushing me on the treadmill, and apply just enough thrust to get the airplane to move 1mph. What is the result of this? We now have an airplane traveling down a treadmill at 1mph because we both agree that the airplane will accelerate under its own thrust. So how fast are the wheels spinning now? Well we started at 10, we added 1mph of forward movement so now we have 11mph of rotational speed on the wheels.

How fast is the treadmill moving now that the wheels are traveling 11mph? That's right, 11mph. Why? because they HAVE to match in order to keep the question intact. There is no way for the treadmill/wheel system to stop the airplanes forward 1mph motion because it's completely reliant on the air that surrounds it. This is no different then starting from a stop.

Now what if the treadmill was traveling in the other direction WITH the airplane? Then the wheels just wont spin at all but the airplane will still accelerate normally because the treadmill is keeping up with the airplanes motion in order to keep the wheels at 0mph. But when the treadmill is in a reverse direction relative to the airplane the speeds MUST double in order to keep the question intact.

Anyway, this is enough for me. I don't think we're going to get anywhere if this doesn't shine the light bulb for you so we can agree to disagree. I had fun though and thanks for being a good sport. I really do enjoy discussions like this as I am hugely into physics and love the very thought provoking nature of this question.

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