You folks seem mechanically-minded...
There is an airplane on a runway. The runway is like a conveyor belt, and can detect the speed of the wheels of the airplane. When the runway senses the wheels moving, the runway will match the speed of the airplane's wheels, but in the opposite direction.
Can this airplane take off?
Discuss.
Sounds like an engineering question....
Here are the givens:
Airplane = A
Runway = R
Conveyor belt = C (C=R)
Wheel speed = WS
Conveyor Speed = CS (Where CS = WS-WS)
Take off speed = TOS
TOS is a direct function of A's design, which is an unknown variable and not given in support of the following question. (airplane could be a glider, or VTOL capable)
No external effects are are defined or placed for the A in the the equation. There is no link between A, and R, C, WS, or CS. You even have to make assumptions about gravity.
The question makes the reader toil over facts given which are irrelevant to A's capability or the forces placed upon it. In fact, the sentences before the question actually have nothing to do with the ending question.
If the plane is capable of flight, it can take off. If incapable, it will not. You can decide on either depending on which assumptions you make about A and forces placed upon it.
Essential missing data:
Does it have thrust against an air medium? (Is there an air medium?) Are the wings strong enough to support the rest of the plane? Are the wheels even free to rotate about an axis attached to the plane. (parking brake applied? If so, neither the wheels or the conveyor surface moves.)
In the end, the real question becomes, do you want the plane to fly or not? Is your glass half empty or half full? You can manufacture either answer depending on the assumptions made, none of which are supported or presented in the original post.
In fact, the question has no relevance to being mechanically minded, either. It is a psychology question to gauge a person' optimism or pessimism.
If you answer no, you're a pessimist.
If you answer yes, you're an optimist.
Unless you have a fear of flying... Then a plane that can't fly is considered a good thing. Ain't it great that it can't crash and kill the occupants. That's optimism!
Cheers,