Calculation of Recoil Velocity

Given:
- Mass of the bullet (m1) = 10 g = 0.01 kg
- Mass of the gun (m2) = 6 kg
- Initial velocity of the bullet (v1) = 300 m/s
- Recoil velocity of the gun (v2) = ?

Using the principle of conservation of momentum:
The total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.

Total momentum before firing:
The total momentum before firing can be calculated by summing the momentum of the bullet and the gun.

Momentum (p) = mass (m) × velocity (v)

The momentum of the bullet (p1) = m1 × v1
The momentum of the gun (p2) = m2 × v2 (since the gun is initially at rest)

Total momentum before firing:
p_total = p1 + p2

Total momentum after firing:
The bullet is fired with a velocity v1, and the gun recoils with a velocity v2. Therefore, the momentum of the bullet and the gun after firing is:

The momentum of the bullet (p1') = m1 × v1'
The momentum of the gun (p2') = m2 × v2'

Total momentum after firing:
p_total' = p1' + p2'

Applying the principle of conservation of momentum:
According to the principle of conservation of momentum, the total momentum before firing is equal to the total momentum after firing.

p_total = p_total'

Therefore,

p1 + p2 = p1' + p2'

Solving for v2:
Substituting the values of p1, p2, p1', and p2' into the equation, we can solve for v2.

m1 × v1 + m2 × 0 = m1 × v1' + m2 × v2'

Since the gun is initially at rest (v2' = 0),

m1 × v1 = m1 × v1' + m2 × 0

Simplifying the equation,

v1' = (m1 × v1) / m1

v1' = v1

Therefore, the recoil velocity of the gun (v2) is equal to the initial velocity of the bullet (v1).

Result:
The recoil velocity of the gun is 300 m/s, which is the same as the initial velocity of the bullet.

Mass of gun = 6 kg (m2)mass of bullet = 10 g = 0.01 kg (m1)u1=u2= 0v1= 300m/sv2 =?
m1 u1 +m2 u2 = m1 v1 + m2 v2 (0.01×0) + (6×0)=(0.01×300) + (6×v2)0 = 3+6v2-3 = 6v2-3/6=v2v2 = -0.5m/s