It should be obvious to everyone that the cart receives both a forward and backward force: The forward force comes from the wind hitting the sail. The backward force comes from the reaction force to the fan blowing air forward.
Basically, the air molecules gave the cart a backward impulse when they departed from the fan, but a forward impulse when they collide with the sail. If the air molecules stick to the sail after collision (perfectly inelastic collision), then the two impulse are equal in magnitude. And the cart will stay at rest. However, if the air molecules rebound backward after collision (elastic collision), then the forward impulse on the sail will be larger than the backward impulse on the fan. And the cart will move forward.
The principle of conservation of momentum can make the analysis even easier. Just use the fact that the total…
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