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.
After firing, bullet and gun momenta are equal and opposite, so that the total momentum remains zero
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To find the initial backward velocity of the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired must be equal to the total momentum after the bullet is fired.
Let's define the initial velocity of the gun as Vg and the initial velocity of the bullet as Vb. The mass of the bullet is 0.45kg, and the mass of the gun is 9kg.
Before the bullet is fired, the gun and the bullet are at rest, so their initial velocities are both 0. Therefore, the total initial momentum is:
Total initial momentum = Mass of the gun * Initial velocity of the gun + Mass of the bullet * Initial velocity of the bullet
Total initial momentum = 9kg * 0 + 0.45kg * 0
Total initial momentum = 0
After the bullet is fired, the gun and the bullet move in opposite directions. Let's assume the backward velocity of the gun is Vg' and the forward velocity of the bullet is Vb'. The total final momentum is:
Total final momentum = Mass of the gun * Final velocity of the gun + Mass of the bullet * Final velocity of the bullet
Total final momentum = 9kg * -Vg' + 0.45kg * Vb'
According to the conservation of momentum, the total initial momentum is equal to the total final momentum, so we have:
0 = 9kg * -Vg' + 0.45kg * Vb'
Now, we can substitute the given values into the equation. The mass of the bullet is 0.45kg, and the initial velocity of the bullet is 200m/s. Therefore, the equation becomes:
0 = 9kg * -Vg' + 0.45kg * 200m/s
0 = -9kg * Vg' + 90kg * m/s
Now we can solve for Vg' by rearranging the equation:
9kg * Vg' = 90kg * m/s
Vg' = 90kg * m/s / 9kg
Vg' = 10m/s
Therefore, the initial backward velocity of the gun is 10 m/s.