Final answer:
To determine the bullet's final speed after it emerges from the block, apply the conservation of momentum and energy principles. Calculate initial momentum, use the vertical rise to find the block's velocity after collision, and solve the final speed of the bullet by equating initial and final momentum.
Step-by-step explanation:
The question involves applying the principles of conservation of momentum and energy conservation in physics. When the bullet of mass 10g strikes the wooden block, we can solve for the final velocity of the bullet by applying the law of conservation of momentum before and after the collision, and the conservation of energy to relate the rise in the block's center of gravity to the velocity of the block (and bullet within it) just after the collision.
To find the initial momentum, multiply the mass and velocity of the bullet: (0.01 kg) x (400 m/s) = 4 kg·m/s. After the collision, the bullet plus block system will have a combined mass of 2.01 kg. Using the given vertical rise, we can calculate the velocity of the block after the collision using potential energy (mgh) and kinetic energy (1/2 m v2).
Finally, applying the momentum equation both before and after the bullet exits the block, and the final kinetic energy of the block, we can solve for the final speed of the bullet after it emerges. The correct choice will be the one that preserves the conservation laws.