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The image contains a physics problem that involves projectile motion. Here’s a breakdown of the problem statement and the information provided:

### Problem:
A bullet is fired from the ground with an initial velocity (\(v_0 = 800 \, \text{m/s}\)) at an angle (\(\alpha = 30^\circ\)) above the horizontal. The effects of air resistance are ignored, and the acceleration due to gravity is taken as \(g = 9.8 \, \text{m/s}^2\). 

The question asks to determine the radius of curvature of the bullet's trajectory at the point of impact.

### Data Provided:
- Initial velocity: \(v_0 = 800 \, \text{m/s}\)
- Launch angle: \(\alpha = 30^\circ\)
- Gravitational acceleration: \(g = 9.8 \, \text{m/s}^2\)
- No air resistance

The answer choices given are:
- a) 78.4 km
- b) 77.4 km
- c) 75.4 km
- d) 76.4 km

### To solve:
The radius of curvature \(R\) of a projectile at any point is given by the formula:

\[
R = \frac{{v^2}}{{g \cdot \cos(\theta)}}
\]

Where:
- \(v\) is the velocity at the point of impact.
- \(g\) is the acceleration due to gravity.
- \(\theta\) is the angle of the trajectory at the point of impact (which, for a parabolic motion, is \(\theta = 0^\circ\), since at the point of impact the trajectory is horizontal).

Let me now calculate this radius.The calculated radius of curvature at the point of impact is approximately 48.98 km. However, this result does not match any of the provided answer choices. It seems there may have been an issue in assumptions or the interpretation of the problem.

Would you like me to revisit or refine any part of this calculation? Let me know if you have any further questions or need more details.

Here are 5 related questions for exploration:
1. How does the launch angle affect the range of a projectile?
2. What is the formula for time of flight in projectile motion?
3. How does the radius of curvature change at different points along the trajectory?
4. What role does air resistance play in real-world projectile motion?
5. How would increasing gravity affect the projectile's range?

**Tip:** In projectile motion, the radius of curvature is smallest at the peak of the trajectory and largest at the points of launch and impact.

A bullet is fired from the ground with an initial velocity of 800 m/s at an angle of 30° above the horizontal. Ignore air resistance and take gravitational acceleration as 9.8 m/s². Determine the radius of curvature of the bullet's trajectory at the point of impact.

Solve a projectile motion problem involving a bullet fired at an initial velocity of 800 m/s at a 30° angle. Learn to calculate the radius of curvature of the bullet's trajectory at the point of impact using kinematic formulas. This problem is ideal for Grade 11-12 students.

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