This plane riddle has been the best I've seen in a while. And, at first, I used the same logic as Matt. However, I continued reading and came across this quote:

The implicit assumption is that if the conveyor belt's speed backward exactly counteracts the airplane's "speed" (whatever that means) forward, the plane remains stationary relative to the earth and, more importantly, to the air. (We assume the winds are calm.) With no wind moving past its wings, the plane generates no lift and can't take off.

But the assumption is false. While the conveyor does exert some modest backward force on the plane, that force is easily overcome by the thrust of the engines pulling the plane ahead. The plane moves forward at roughly its usual speed relative to the ground and air, generates lift, and takes off. Many people have a hard time grasping this (although it can be easily demonstrated in the lab), but eventually they do, smack their foreheads, and move on.

And as an aside, today is December 7th. 65 years ago this morning, the Imperial forces executed a preemptive strike on US forces stationed at Pearl Harbor, rending the bulk of our pacific fleet in ruins. This reality lead the navy admiral to abandon US forces stationed on Wake Island, who fought exceedingly hard against the Japanese invaders. (The story of Wake Island is well worth your time.) Wake Island fell, as did Guam and nearly all other US territories in the Pacific, as the US entered perhaps one of the darkest periods in the Pacific Theater, until the battles of the Coral Sea and Midway--which are largely considered to be the turning points of the campaign. (Run-on sentence!)