Question

a 10 gram Bullet is shot from a 5 kg gun with a velocity of 400 m per second what is the speed of the gun ?

Answer 1

According to law of conservation of linear momentum
M1(V1)=M2(V2) where M1 is the mass of the bullet,V1 is the velocity of the bullet,M2 is the mass of the gun and V2 is the recoil velocity of the gun.
10(400)=5000V2
V2=4000÷5000
V2= 0.8 m/ sec

Answer 2

suppose, m = mass, u = initial velocity, v = final velocity
now,
bullet's, m1 = 10/1000 = .01kg
gun's, m2 = 5 kg
bullet's, u1 = 0 m/s
gun's, u2 = 0 m/s
bullet's, v1 = 400 m/s
gun's, v2 = ?

# m1 x u1 + m2 x u2 = m1 x v1 + m2 x v2
or, .01 x 0 + 5 x 0 = .01 x 400 + 5 x v2
or, 0 = 4 + 5 x v2
or, v2 = -0.8m/s

so the speed is 0.8 m/s.

Hope this helps you :)