Statement I: If a particle projected horizontally just above, the surface of the earth with a speed greater than escape speed, then it will escape from gravitational influence of the earth. Assume that particle has a clear path.
Statement II: Escape velocity is independent of its direction.

Options

A. Statement I is True, Statement II is True: Statement II is a correct explanation for Statement I.
B. Statement I is True, Statement II is True: Statement II is Not a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To solve the question, we need to analyze both statements provided:

**Statement I:** If a particle is projected horizontally just above the surface of the Earth with a speed greater than escape speed, then it will escape from the gravitational influence of the Earth, assuming that the particle has a clear path.

**Statement II:** Escape velocity is independent of its direction.

### Step-by-Step Solution:

1. **Understanding Escape Velocity:**
- Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any additional propulsion.
- For Earth, the escape velocity is approximately 11.2 km/s.

2. **Analyzing Statement I:**
- If a particle is projected horizontally with a speed greater than the escape velocity, it means that the particle has enough kinetic energy to overcome the gravitational potential energy of the Earth.
- Therefore, the particle will indeed escape the gravitational influence of the Earth, provided there are no other forces acting on it (like air resistance or obstacles).

3. **Analyzing Statement II:**
- Escape velocity is a scalar quantity and does not depend on the direction of the projection. Whether the object is thrown vertically, horizontally, or at any angle, as long as it reaches the escape velocity, it will escape Earth's gravity.
- This confirms that escape velocity is independent of direction.

4. **Conclusion:**
- Both statements are true. Statement II correctly explains Statement I, as it clarifies that the direction of projection does not affect the escape velocity.

### Final Answer:
- Statement I is true.
- Statement II is true.
- Statement II is the correct explanation for Statement I.

Thus, the correct option is: **Option 1: Statement I is true. Statement II is true. Statement II is the correct explanation for Statement I.**