Thanks for any help. Here is the momentum example: Alice obtains a fire extinguisher which she holds firmly on her office chair.
Suppose Alice opens the nozzle of the fire extinguisher so that it ejects gas at a constant rate (mass per unit time) and constant speed. How will Alice move? The answer for the example was that she accelerates backwards.
I see the answer by using momentum with . Since the rate of release and the speed are kept constant the numerator is constant. Since Alice's mass includes her chair and the extinguisher (which is getting used up) the denominator is getting smaller so that Alice's velocity is actually increasing (so she is accelerating). But if I try to use impulse with I actually get an answer that she doesn't accelerate backwards. should be 0 because the gas's speed is constant and if velocity is constant then its derivative acceleration is 0. Hence which means that she is not accelerating. Can someone point out what I'm missing? Thanks.