To determine the velocity of the bullet, we can apply the principle of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision. Assuming the bullet and the block are the only objects involved in the system:
Initial momentum = Final momentum
The initial momentum can be calculated as the product of the mass and velocity of the bullet before the collision, while the final momentum is the product of the combined mass (bullet + block) and the final velocity after the collision.
Given: Mass of the bullet (m₁) = 100 g = 0.1 kg Mass of the block (m₂) = 12 kg Initial velocity of the bullet (v₁) = ? Final velocity of the combined bullet and block (v₂) = 0 (since the system comes to rest)
Using the conservation of momentum equation:
m₁ * v₁ = (m₁ + m₂) * v₂
0.1 kg * v₁ = (0.1 kg + 12 kg) * 0
0.1 kg * v₁ = 0 kg
Since the mass of the bullet is nonzero and the final velocity is zero, it implies that the initial velocity of the bullet (v₁) must also be zero.
Hence, the velocity of the bullet before the collision is 0 m/s.