A spring loaded 100g dart gun is affixed at rest on a 150g frictionless cart. It fires a 25g dart with a velocity of 30 m/s. What is the final momentum of the system?

I'm confused as to whether or not I should use conservation of momentum or center of mass, and I'm not really sure what to do if it is center of mass...

Thank you!

3 answers

ZERO !!
The final momentum =initial momentum
Which IS ZERO

if you want the speed backwards of the cart then
250 v + 25 * 30 = 0

so the momentum of the cart is 250 v
By the way the center of mass of the SYSTEM (not the cart) also does not move because there is no external force on the SYSTEM.
The car moves back as the dart moves forward to keep the momentum and center of gravity the same before and after.
Thank you!