# Conservation of Momentum - classic example [duplicate]

Suppose we have the following set-up, or rather a boat is a bit easier:

The question is whether the boat moves forward, the answer is yes. My thought was, the momentum is conserved. So, say the mass of the air generated by the ventilator is $$m$$ and the velocity of the air is $$v$$, the weight of both the boat and the person is $$M$$ and the velocity of the system is $$u$$. Then

$$P_1=P_2 \Rightarrow m\cdot v=M\cdot u$$

If we consider the velocity of the wind pushed back by the sail in the positive direction, then $$u$$ would be in the opposite direction which means the system moves to the right.

However, in the solutions it says:

Let $$P$$ denote the momentum generated by the air molecules and assume these molecules would hit the sail elastically, then the momentum should experience a change of $$2P$$ and cause a resultant momentum of $$P$$ in the opposite direction.

But i don't really understand this solution...If someone could clear that up I would be very grateful...