Assertion In projectile motion, if time of flight is 4s, then maximum height will be 20 m. (Take, `g = 10 ms^(-2))`
Reason Maximum height `= (gT)/(2)`.

Options

A. If both Asseration and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is false
D. If Assertion is false but Reason is true

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided in the question regarding projectile motion.

### Step-by-Step Solution:

1. **Understanding Time of Flight**:
The time of flight (T) for a projectile is given by the formula:
\[ T = \frac{2u \sin \theta}{g} \]
where \( u \) is the initial velocity, \( \theta \) is the angle of projection, and \( g \) is the acceleration due to gravity.

2. **Given Values**:
We are given that the time of flight \( T = 4 \) seconds and \( g = 10 \, \text{m/s}^2 \).

3. **Finding \( u \sin \theta \)**:
Rearranging the time of flight formula to find \( u \sin \theta \):
\[ u \sin \theta = \frac{gT}{2} \]
Substituting the values:
\[ u \sin \theta = \frac{10 \times 4}{2} = 20 \, \text{m/s} \]

4. **Maximum Height Formula**:
The formula for maximum height (H) reached by a projectile is:
\[ H = \frac{(u \sin \theta)^2}{2g} \]

5. **Substituting \( u \sin \theta \)**:
Now substituting \( u \sin \theta = 20 \, \text{m/s} \) into the maximum height formula:
\[ H = \frac{(20)^2}{2 \times 10} = \frac{400}{20} = 20 \, \text{m} \]

6. **Conclusion on Assertion**:
The assertion states that if the time of flight is 4 seconds, then the maximum height will be 20 m. From our calculations, we find that this is indeed correct.

7. **Analyzing the Reason**:
The reason provided states that maximum height \( H = \frac{gT}{2} \). This is incorrect. The correct formula, as derived, is \( H = \frac{gT^2}{8} \). Thus, the reason is false.

8. **Final Evaluation**:
Since the assertion is true and the reason is false, the correct conclusion is that the assertion is correct but the reason is not.

### Final Answer:
- Assertion: True
- Reason: False
- Therefore, the correct option is that the assertion is true, but the reason is false.