Nick_Tarleton comments on The Correct Contrarian Cluster - Less Wrong
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This ignores mass. Thrust is (mass flow rate) * v_air, so it can get enough thrust by moving enough air at a velocity less than v_car. As for energy, power = 1/2 * F * v for air or car, so again, you can get enough thrust if v_air < v_car.
There's no perpetual motion, because as the originally linked solution says, eventually the apparent headwind becomes too strong. (The above assumes apparent wind is zero.)