**Using Energy Laws to Determine the Emerging Velocity of a Bullet**

To find the emerging velocity of a bullet after penetrating a block of wood, we will make use of the principles of energy conservation. The law of conservation of energy states that the total energy of a closed system remains constant over time. In this case, the closed system is the bullet and the block of wood.

**Given Data:**
- Mass of the bullet (m) = 90 g = 0.09 kg
- Initial velocity of the bullet (u) = 300 m/s
- Penetration depth into the block of wood (d) = 10 m

**Step 1: Calculate the Initial Kinetic Energy of the Bullet**
The initial kinetic energy (KE) of the bullet can be calculated using the formula:

KE = 0.5 * m * u^2

Substituting the given values, we have:

KE = 0.5 * 0.09 kg * (300 m/s)^2

**Step 2: Calculate the Work Done by the Bullet**
The bullet does work against the resistance of the wood as it penetrates into it. The work done (W) can be calculated using the formula:

W = force * distance

In this case, force is the resistance force exerted by the wood, and distance is the penetration depth. Since the force is constant, we can rewrite the formula as:

W = force * distance = average force * penetration depth

**Step 3: Calculate the Average Force Exerted by the Wood**
The average force exerted by the wood can be calculated using the formula:

average force = change in momentum / time

Since the bullet comes to rest inside the wood, the change in momentum is given by:

change in momentum = m * (final velocity - initial velocity)

The time taken for the bullet to come to rest can be calculated using the formula:

time = distance / final velocity

**Step 4: Calculate the Final Velocity of the Bullet**
Using the principle of conservation of energy, we know that the work done by the bullet is equal to the change in kinetic energy:

W = KE - change in KE

Solving for the final velocity (v) of the bullet after penetrating the wood, we have:

v = sqrt(2 * W / m)

**Step 5: Apply the Calculations to the Given Scenario**
In the given scenario, we have a second block of wood with a thickness of 5 m. Using the same calculations as above, we can determine the final velocity of the bullet after penetrating this block.

**Conclusion**
By applying the principles of energy conservation and the laws of motion, we can determine the emerging velocity of a bullet after penetrating a block of wood. By following the steps outlined above and performing the necessary calculations, we can find the final velocity for different scenarios.