Cannon firing cannonballs inside a sealed railroad car

[Destrio]

A second systems of particles question I'm stuck on:

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

 

[Destrio]

P = (Mtotal)(Vcm)
Vcm = (1/Mtotal)ΣmnVn

for each ball fired:

let M be cannon and car
let m be cannonballs

Pfx = MVx + mv(with respect to the earth)x = MVx + m(vx +Vx)

ΣFext,x = 0
so Pix = Pfx

Mvx + m(vx +Vx) = 0

Vx = -mvx/(M+m)

so

Vcm = (1/Mtotal)ΣmnVn
Vcm = (1/Mtotal)Σ(M+m)[-mvx/(M+m)]
Vcm = (1/Mtotal)Σ(-mvx)

is this correct so far?

 

[Destrio]

Do I want to be solving for Vcm or the position of the centre of mass initially?

 

[Helical]

It seems to me that this is less question about momentum and more a question of forces. Also you did not include how many cannonballs there are, which seems to be important information for both A and B.
Perhaps I'm wrong though.

 

[Destrio]

the question doesn't state a number of cannonballs
i think we just use n number of cannonballs