A gun of mass 0.1kg has a bullet of mass 0.1kg the bullet leaves the piston when fired at a velocity of 200m/s find the final velocity?
To find the final velocity, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.
The momentum of an object can be calculated by multiplying its mass by its velocity. In this case, the total momentum before firing the bullet is zero because both the gun and bullet are at rest. After the bullet is fired, the momentum of the gun will be zero because it is assumed to have a much larger mass and negligible velocity.
Therefore, we can write the conservation of momentum equation as:
(0.1 kg bullet mass) x (200 m/s bullet velocity) = (0.1 kg bullet mass + 0.1 kg gun mass) x (final velocity)
Now, we can solve for the final velocity:
(0.1 kg x 200 m/s) = (0.1 kg + 0.1 kg) x final velocity
20 kg m/s = 0.2 kg x final velocity
final velocity = (20 kg m/s) / (0.2 kg)
final velocity = 100 m/s
Therefore, the final velocity of the bullet after it leaves the piston when fired is 100 m/s.