To calculate the recoil 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 is equal to the total momentum after the bullet is fired.
The momentum of an object is given by the product of its mass and velocity. Therefore, the initial momentum of the system (bullet + gun) is:
Initial momentum = (mass of bullet) × (velocity of bullet) + (mass of gun) × (velocity of gun)
Given: Mass of bullet = 15 g = 0.015 kg Velocity of bullet = 400 m/s Mass of gun = 6 kg Velocity of gun = ?
Using the conservation of momentum, we can set up the equation:
(Initial momentum) = (Final momentum)
(0.015 kg × 400 m/s) + (6 kg × 0) = (0 × final velocity of gun) + (6 kg × final velocity of gun)
0.015 kg × 400 m/s = 6 kg × final velocity of gun
0.006 kg m/s = 6 kg × final velocity of gun
final velocity of gun = (0.006 kg m/s) / 6 kg
final velocity of gun = 0.001 m/s
Therefore, the recoil velocity of the gun is approximately 0.001 m/s.