B

Step 1: Calculate the initial kinetic energy of the bullet.
The mass of the bullet, m = 50.0 g = 0.050 kg.
The initial speed, v_i = 200 m/s.
The initial kinetic energy (KE_initial) is given by the formula:
$$ KE_{initial} = \frac{1}{2} mv_i^2 $$
Substituting the values:
$$ KE_{initial} = \frac{1}{2} (0.050)(200)^2 = \frac{1}{2} (0.050)(40000) = 1000 \text{ J} $$
Step 2: Determine the final kinetic energy after the bullet emerges.
The problem states that the bullet retains 10% of its initial kinetic energy after passing through the plywood.
Thus,
$$ KE_{final} = 0.10 \times KE_{initial} = 0.10 \times 1000 = 100 \text{ J} $$
Step 3: Use the final kinetic energy to calculate the final speed of the bullet.
The final kinetic energy is also given by the formula:
$$ KE_{final} = \frac{1}{2} mv_f^2 $$
Rearranging for final speed, v_f:
$$ v_f = \sqrt{\frac{2 \times KE_{final}}{m}} $$
Substituting the values:
$$ v_f = \sqrt{\frac{2 \times 100}{0.050}} = \sqrt{4000} = 63.25 \text{ m/s} $$
Therefore, the emergent speed of the bullet is approximately 63.25 m/s.