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No is not correct. Yes is the correct answer because the rearward thrust from the engines(s) of the airplane would move the airplane forward and the wheels would only spin faster on the tredmill.

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Q: Can an airplane take off when it is on a treadmill going the opposite direction?
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Will an Airplane takeoff on a treadmill if the Airplanes thrust was matched to the treadmills speed?

In this case no. For an aircraft to fly it needs airflow over the wings. In this situation the thrust is being used to keep up with motion of treadmill and not going towards moving air over the wings. this will mean no lift is produced and therefore it wont take off.