a bullet of mass 0.045kg is fire from a gun of mass 9kg the bullet moving with an initia valocity of 200ms. find the initial backward velocity of the gun
conserve momentum.
0.045*200 = 9v
To find the initial backward velocity of the gun, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the firing and after the firing remains constant.
The momentum of an object is given by the product of its mass and velocity (p = m * v).
Before firing, the total momentum is zero because the gun and bullet are at rest. After firing, the total momentum must still be zero because there is no external force acting on the system.
Let's denote the initial backward velocity of the gun as "v_gun" and the final velocity of the bullet as "v_bullet."
Using the conservation of momentum, we can write the equation:
(m_gun * v_gun) + (m_bullet * v_bullet) = 0
Where:
- m_gun is the mass of the gun (9 kg)
- v_gun is the initial backward velocity of the gun (what we want to find)
- m_bullet is the mass of the bullet (0.045 kg)
- v_bullet is the initial velocity of the bullet (200 m/s)
Substituting the known values, we get:
(9 kg * v_gun) + (0.045 kg * 200 m/s) = 0
Simplifying the equation:
9 kg * v_gun = -0.045 kg * 200 m/s
Dividing both sides by 9 kg:
v_gun = (-0.045 kg * 200 m/s) / 9 kg
Calculating the result:
v_gun = -1 m/s
Therefore, the initial backward velocity of the gun is -1 m/s. The negative sign indicates that the gun moves in the opposite direction to the bullet.