A bullet of mass 0.45kg is fired from a gun of mass 9kg,the bullet moving with an initial velocity of 200meter per sec. Find the initial backward velocity of the gun.

Duplicate question; already answered.

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To determine the initial backward velocity of the gun, we can use the principle of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting.

In this case, the total momentum before firing the bullet is zero since both the bullet and the gun are at rest. After firing the bullet, the bullet and gun move in opposite directions, so their momenta will have opposite signs.

We can express the conservation of momentum as follows:

(mass of bullet) × (velocity of bullet) = -(mass of gun) × (velocity of gun)

Let's substitute the given values into the equation:

(0.45 kg) × (200 m/s) = -(9 kg) × (velocity of gun)

Simplifying the equation, we have:

90 kg·m/s = -(9 kg) × (velocity of gun)

Dividing both sides by -9 kg:

velocity of gun = -10 m/s

Therefore, the initial backward velocity of the gun is 10 m/s. The negative sign indicates that the gun moves in the opposite direction of the bullet.