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A cannon and supply of cannonballs are inside a sealed railroad car of length L. The cannon fires to the right; the car recoils to the left. The cannonballs remain in the car after hitting the far wall.

a) After all the cannonballs have been fired, what is the greatest distance the car can have moved from its original position?

b) What is the speed of the car after all the cannonballs have been fired?

So I figure that the centre of mass will be changing after each cannonballs is fired. But also we need to conserve momentum with each cannonball fired?

Where do I need to start? Should I worry about conservation of momentum first? Or concern myself with determining the centre of mass after each shot first?

Thanks