Can a plane taxiing on a backward-moving conveyor belt take off? This would seem to be a standard artificial end-of-chapter physics problem, but it escaped to the internet and became a controversy. To those who understand about relative velocity (and who know that thrust is generated by the air moved by a plane’s jet or prop), the answer is pretty straightforward, but you can check out the Mythbusters test (parts one and two) to make sure.
On further reflection, perhaps “straightforward” is overly optimistic. But you should be able to see why a real plane can take off, even taxiing against a moving conveyor, and how the question generated so much froth on the intertubes due to its ambiguous wording.
