Assertion : If time of flight in a projectile motion is made two times, its maximum height will become four times.
Reason : In projectile motion `H prop T^2` , where H is maximum height and T the time of flight.

Options

A. (a)If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b)If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false, but the Reason is true.

Explanation

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

### Step-by-Step Solution:

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

2. **Understanding Maximum Height**:
The maximum height \( H \) reached by the projectile can be calculated using the formula:
\[ H = \frac{u^2 \sin^2 \theta}{2g} \]

3. **Proportionality of Height to Time of Flight**:
From the time of flight equation, if we double the time of flight \( T \) (i.e., \( T' = 2T \)), we can relate it to the maximum height:
\[ H' = \frac{(u \sin \theta)^2}{2g} \left(\frac{T'}{T}\right)^2 \]
Since \( T' = 2T \), we have:
\[ H' = \frac{u^2 \sin^2 \theta}{2g} \cdot 4 = 4H \]
This shows that if the time of flight is doubled, the maximum height becomes four times the original height.

4. **Conclusion on Assertion and Reason**:
- The assertion states that if the time of flight is made two times, the maximum height will become four times. This is **true**.
- The reason states that in projectile motion, \( H \) is proportional to \( T^2 \). This is also **true**.

5. **Final Evaluation**:
Both the assertion and reason are true, and the reason correctly explains the assertion. Therefore, the correct conclusion is that both statements are true and the reason is a correct explanation of the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason is a correct explanation of the assertion.