Question

Shell of mass 10kg is fired from a gun of mass 600 kg the gun recoils with a velocity of 6 m per second find the muzzle velocity of the shell

Answer 1

This problem is based on conservation of momentum.
(Momentum= mass*velocity )
total momemtum before firing= total momemtum after firing.
BEFORE:
*total momentum= momentum of gun + momentum of shell or bullet
= MV +mu
=0 (because before firing both velocities are zero since they are at rest)
(let M= mass of gun
V=velocity of gun
m =mass of shell
u=velocity of shell)

AFTER:
*totalmomentum = MV +mu
=600*(-6) + 10*u

(-6 is because it is recoil . direction is opposite)

now
based on conservation of momentum.
ie total momemtum before firing= total momemtum after firing.
0= 600*(-6) + 10*u
-10u=-3600
u=-3600/-10
u =360m/s
so muzzle velocity of shell is 360m/s