Assertion The maximum height of projectile is always 25% of the maximum range.
Reasons For maximum range, projectile should be projected at `90^(@)`

Options

A. Both Assertion and Reason are correct, Reason is the coreect expianation of Assertion
B. Bioth Assertion and Reason are Correct but Reason is not the correct expalnation of Assertion
C. Assetion is correct and Reason is incorrect
D. Assertion is incorrect and Reason is correct

Answer

To solve the problem, we need to analyze the assertion and the reason given in the question.

### Step 1: Understanding the Assertion
The assertion states that the maximum height of a projectile is always 25% of the maximum range.

### Step 2: Formulas for Maximum Height and Range
1. **Maximum Range (R)** of a projectile is given by the formula:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]
For maximum range, the angle \(\theta\) should be \(45^\circ\) because \(\sin(90^\circ) = 1\). Thus, the maximum range becomes:
\[ R_{\text{max}} = \frac{u^2}{g} \]

2. **Maximum Height (H)** of a projectile is given by the formula:
\[ H = \frac{u^2 \sin^2(\theta)}{2g} \]
At \(\theta = 45^\circ\), we have:
\[ H = \frac{u^2 \sin^2(45^\circ)}{2g} = \frac{u^2 \left(\frac{1}{\sqrt{2}}\right)^2}{2g} = \frac{u^2 \cdot \frac{1}{2}}{2g} = \frac{u^2}{4g} \]

### Step 3: Relating Maximum Height to Maximum Range
From the above calculations, we can relate the maximum height \(H\) to the maximum range \(R_{\text{max}}\):
\[ H = \frac{u^2}{4g} \quad \text{and} \quad R_{\text{max}} = \frac{u^2}{g} \]
Now, if we express \(H\) in terms of \(R_{\text{max}}\):
\[ H = \frac{R_{\text{max}}}{4} \]
This shows that the maximum height is indeed 25% of the maximum range.

### Step 4: Analyzing the Reason
The reason states that for maximum range, the projectile should be projected at \(90^\circ\). This is incorrect because the angle for maximum range is actually \(45^\circ\).

### Conclusion
- The assertion is **correct**: The maximum height of a projectile is always 25% of the maximum range.
- The reason is **incorrect**: The angle for maximum range is \(45^\circ\), not \(90^\circ\).

Thus, the correct answer is that the assertion is true, but the reason is false.

### Final Answer
Assertion is correct, but the reason is incorrect.

---