Final answer:
The problem of determining how high the block will rise after being struck by a bullet involves conserving momentum during the collision and conserving energy to find the maximum height in a Physics context.
Step-by-step explanation:
The student's question concerns a scenario where a bullet is fired into a block of wood, and the block is propelled upward by the collision. To find out how high the block will rise after the bullet becomes embedded in it, we must apply the principle of conservation of momentum for the collision and the conservation of energy to find the maximum height reached by the block. Initially, we calculate the combined momentum of the bullet and block system just after the collision using the initial velocity of the bullet and the fact that the block was at rest before the collision. This is given by the formula m_bullet * v_bullet, where m_bullet is the mass of the bullet and v_bullet is the velocity of the bullet just before impact. Next, we use the conservation of momentum to find the velocity of the block with the embedded bullet right after the impact. As both the block and the bullet move together after the collision, we apply the following formula: m_block + m_bullet * v_final_block_bullet = m_bullet * v_bullet. Solving for v_final_block_bullet gives us the velocity of the block-bullet system immediately after the collision. Then, we utilize the conservation of energy, considering that the kinetic energy of the block and bullet system will be entirely converted into gravitational potential energy at the maximum height. The formula used is KE_initial = PE_final, where KE_initial is the initial kinetic energy, and PE_final is the gravitational potential energy at maximum height. This can be expressed by 1/2 * (m_block + m_bullet) * v_final_block_bullet^2 = (m_block + m_bullet) * g * h, where g is the acceleration due to gravity, and h is the height. From this equation, we can solve for h, the maximum height the block will reach.