Final answer:
The appropriate principle to analyze the situation is the conservation of momentum. We can use this principle to solve the unknowns in the problem.
Step-by-step explanation:
In this case, the appropriate principle to analyze the situation is the conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision. We can use this principle to solve the unknowns in the problem. First, we need to find the initial momentum of the bullet-block system before the collision. Since the bullet is fired into the block, both the block and the bullet are assumed to be at rest before the collision. Therefore, the initial momentum is zero.
After the collision, the bullet becomes embedded in the block, so the two objects stick together and move as a single system. The final velocity of the combined bullet-block system can be found using the conservation of momentum equation: m_bullet * v_bullet + m_block * v_block = (m_bullet + m_block) * v_final, where m_bullet and m_block are the masses of the bullet and the block, v_bullet and v_block are their respective velocities before the collision, and v_final is the final velocity of the combined system after the collision.