the muzzle velocity of a 50.0g shell leaving a 3.00kg rifle is 400 m/s what is the recoil velocity of the rifle

Answer 1

Conservation of Momentum says m1v1+m2v2 (before collision) = m1v1+m2v1 (after)
In this problem you're given that the bullet and the gun are of one mass before the collision, and are sitting still, which cancels out the first half of the equation.
This leaves you with m1v1 = -m2v2
(.05kg)*(400m/s) = -(3kg)*v2
solve for v2 and you get -6.67m/s

Answer 2

6.00