I have an extremely intelligent friend that simply cannot wrap his head around this problem. He is just having a hard time separating airspeed from ground speed. For some reason he's having a mental block about the air above the belt not moving WITH the belt.
Instead of a conveyor belt, explain it as taking off on a sheet of ice. It is the same principle as the conveyor belt without all the extra red herrings of friction, belt speed, etc thrown in.
Oh! I like that twist! Then you can ask the question "How long is the landing rollout on ice?" Answer: the same length as if you didn't touch the brakes on a normal landing. lol