Yes, this is what I think, another thing is I have read an airplane takes less time travelling from New York to LA than from LA to New York because of the earth's spin. If it were flat this could not happen, if it spins it has to be round or close to round.
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To be precise, the airplane travel-time thing is not directly because of the spin - it's because the prevailing winds blow West to East (which, by the way, means that LA->NY is the shorter trip, not the other way around). The wind direction is certainly influenced by the Earth's spin, but not necessarily in ways that are obvious to a layperson.
My point is that you need to be careful when using arguments like these; an experienced flat-earther will likely be able to turn a not-quite-precise argument like this against you if you're unprepared.
No, what I read is since the airplane is flying at 30,000 feet, the earth's movement does not influence it so much so the earth spinning from west to east makes the distance shorter when going westward as the west is coming towards the plane when the plane is going to the east the target point is actually moving away , I think I would have to go into diagrams to show this, but you can look it up.