To find the speed of recoil of the gun, we can apply the law of conservation of momentum. According to this law, 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. Let's denote the mass of the bullet as m_bullet, the mass of the gun as m_gun, the initial velocity of the bullet as v_bullet, and the recoil velocity of the gun as v_gun.
Before the bullet is fired, the total momentum is zero because both the bullet and the gun are at rest:
Total momentum before = (m_bullet + m_gun) * 0 = 0
After the bullet is fired, the total momentum is:
Total momentum after = m_bullet * v_bullet + m_gun * v_gun
Since the total momentum before and after must be the same, we can set up the equation:
0 = m_bullet * v_bullet + m_gun * v_gun
Now we can plug in the given values:
m_bullet = 0.004 kg (4.0 gm converted to kg) v_bullet = 600 m/s m_gun = 5.0 kg
0 = (0.004 kg) * (600 m/s) + (5.0 kg) * v_gun
Solving for v_gun:
(0.004 kg) * (600 m/s) = (5.0 kg) * v_gun
v_gun = (0.004 kg * 600 m/s) / (5.0 kg)
v_gun ≈ 0.48 m/s
Therefore, the speed of recoil of the gun is approximately 0.48 m/s.