In ground to ground projectile motion under gravity, which of the following doesn't affect the time of flight ?

Options

A. rotaton of earth
B. air resistance
C. curvature of earth
D. all of these

Answer

To solve the question regarding which factor does not affect the time of flight in ground-to-ground projectile motion under gravity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Time of Flight**:
The time of flight (T) for a projectile launched from the ground and returning to the ground can be expressed by the formula:
\[ T = \frac{2u \sin \theta}{g} \]
where:
- \( u \) = initial velocity,
- \( \theta \) = angle of projection,
- \( g \) = acceleration due to gravity.

2. **Identify the Variables**:
From the formula, we can see that the time of flight depends on:
- The initial velocity \( u \),
- The angle of projection \( \theta \) (specifically \( \sin \theta \)),
- The acceleration due to gravity \( g \).

3. **Analyze the Given Options**:
We need to determine which of the following does not affect the time of flight:
- Initial velocity \( u \)
- Angle of projection \( \theta \)
- Acceleration due to gravity \( g \)
- Rotation of the Earth

4. **Evaluate Each Factor**:
- **Initial Velocity \( u \)**: Affects time of flight directly as seen in the formula.
- **Angle of Projection \( \theta \)**: Affects time of flight through \( \sin \theta \).
- **Acceleration due to Gravity \( g \)**: Affects time of flight inversely.
- **Rotation of the Earth**: The rotation of the Earth does not affect the time of flight in the ideal case of projectile motion. The time of flight is determined by the initial conditions and not by the rotational motion of the Earth.

5. **Conclusion**:
Based on the analysis, the factor that does not affect the time of flight is the **rotation of the Earth**.

### Final Answer:
The correct option is **the rotation of the Earth**.

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