Understanding the Problem
To determine the minimum number of lines required to stop a bullet that loses 50% of its velocity as it passes through each line, we can analyze the velocity reduction through successive lines.

Initial Conditions
- Let the initial velocity of the bullet be \( V_0 \).
- After passing through the first line, the velocity becomes \( V_1 = \frac{1}{2} V_0 \).
- After passing through the second line, the new velocity is \( V_2 = \frac{1}{2} V_1 = \frac{1}{4} V_0 \).
- Continuing this process, after \( n \) lines, the velocity is given by the formula:
\( V_n = \left(\frac{1}{2}\right)^n V_0 \).

Stopping Condition
To completely stop the bullet, we need to reduce its velocity to 0. However, in practical terms, we can consider it "stopped" when its velocity approaches a negligible value.

Mathematical Analysis
- We want \( V_n \) to become very small or effectively 0. Thus, we need:
\( \left(\frac{1}{2}\right)^n V_0 < \epsilon="" \)="" (where="" \(="" \epsilon="" \)="" is="" a="" very="" small="" />
- Rearranging gives:
\( n > \log_{1/2} \left(\frac{\epsilon}{V_0}\right) \).

Conclusion
Since each line reduces the velocity by half, the number of lines \( n \) needed to bring the bullet's velocity to a negligible level increases logarithmically with the initial velocity. Therefore, the minimum number of lines required can be approximated as follows:
- If you want to stop the bullet completely, you would need at least **n = 10** lines, assuming a practical threshold for negligible velocity.
This ensures that after passing through 10 lines, the bullet's velocity is effectively reduced to nearly 0.