Mass of gun * velocity of gun = mass of bullet * velocity of bullet
6*v=50/1000*400
6v=0.05*400
6v=5/100*400
6v=5*4
v=20/6
v=3.33333

Answer:

Explanation:

The law of conservation of momentum states that the total momentum of a system remains constant if no external force acts on it. This means that the momentum of the bullet and the gun before firing will be equal to the momentum of the bullet and the gun after firing.

Step 1: Calculate the momentum of the bullet before firing.

Momentum (p) = mass (m) x velocity (v)
p = 0.05 kg x 400 m/s
p = 20 kg m/s

Step 2: Calculate the momentum of the gun before firing.

Momentum (p) = mass (m) x velocity (v)
p = 6 kg x 0 m/s
p = 0 kg m/s

Step 3: Calculate the total momentum of the system before firing.

Total momentum (p) = momentum of bullet + momentum of gun
p = 20 kg m/s + 0 kg m/s
p = 20 kg m/s

Step 4: Calculate the momentum of the bullet after firing.

Momentum (p) = mass (m) x velocity (v)
p = 0.05 kg x -v
p = -0.05v kg m/s

Step 5: Calculate the momentum of the gun after firing.

Momentum (p) = mass (m) x velocity (v)
p = 6 kg x v'
p = 6v' kg m/s

Step 6: Calculate the total momentum of the system after firing.

Total momentum (p) = momentum of bullet + momentum of gun
p = -0.05v kg m/s + 6v' kg m/s

Step 7: Apply the law of conservation of momentum.

Total momentum before firing = Total momentum after firing
20 kg m/s = -0.05v kg m/s + 6v' kg m/s

Step 8: Solve for v'.

20 kg m/s = -0.05v kg m/s + 6v' kg m/s
20 kg m/s = (6v' - 0.05v) kg m/s
20 kg m/s = 5.95v' kg m/s
v' = 3.36 m/s

Therefore, the recoil velocity of the gun is 3.36 m/s in the opposite direction to the bullet.