**Using Energy Laws to Solve the Problem:**

To solve this problem, we can apply the principle of conservation of energy. By considering the initial kinetic energy of the bullet and the work done in penetrating the wood, we can determine the emerging velocity of the bullet.

**Given Data:**
- Mass of the bullet (m) = 90 g = 0.09 kg
- Initial velocity of the bullet (u) = 300 m/s
- Penetration depth in the first block of wood (d1) = 10 m
- Thickness of the second block of wood (d2) = 5 m

**Step 1: Calculating the Initial Kinetic Energy of the Bullet:**

The initial kinetic energy (KE) of the bullet can be calculated using the formula:

KE = (1/2) * m * u^2

Substituting the given values, we get:

KE = (1/2) * 0.09 kg * (300 m/s)^2

KE = 4050 J

**Step 2: Calculating the Work Done in Penetrating the Wood:**

The work done (W) in penetrating the wood can be calculated using the formula:

W = Force * Distance

Since the only force acting on the bullet is the friction between the bullet and the wood, we can calculate the work done as the product of the force of friction and the penetration depth.

W = μ * m * g * d1

where:
- μ is the coefficient of friction between the bullet and the wood
- g is the acceleration due to gravity

**Step 3: Calculating the Coefficient of Friction:**

We need to determine the coefficient of friction (μ) between the bullet and the wood. The coefficient of friction can vary depending on the type of wood and the surface conditions. Therefore, we need to refer to experimental data or make an assumption based on similar scenarios.

Let's assume the coefficient of friction (μ) to be 0.3.

**Step 4: Calculating the Work Done:**

Substituting the given values, we get:

W = 0.3 * 0.09 kg * 9.8 m/s^2 * 10 m

W = 26.46 J

**Step 5: Applying the Principle of Conservation of Energy:**

According to the principle of conservation of energy, the initial kinetic energy of the bullet is equal to the sum of the work done in penetrating the wood and the final kinetic energy of the bullet.

KE = W + (1/2) * m * v^2

where:
- v is the emerging velocity of the bullet

Substituting the known values, we have:

4050 J = 26.46 J + (1/2) * 0.09 kg * v^2

**Step 6: Calculating the Emerging Velocity of the Bullet:**

Rearranging the equation, we get:

(1/2) * 0.09 kg * v^2 = 4050 J - 26.46 J

(1/2) * 0.09 kg * v^2 = 4023.54 J

v^2 = (4023.54 J * 2) / (0.09 kg)

v^2 = 89345.33 m^2/s^2

v =