Assertion: For projection angle `tan^(-1)(4)`, the horizontal range and the maximum height of a projectile are equal.
Reason: The maximum range of projectile is directely proportional to square of velocity and inversely proportional to acceleration due to gravity.

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 given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that for a projection angle of \( \tan^{-1}(4) \), the horizontal range and the maximum height of a projectile are equal.

2. **Formulas for Horizontal Range and Maximum Height**:
- The formula for the horizontal range \( R \) of a projectile is given by:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]
- The formula for the maximum height \( H \) is given by:
\[ H = \frac{u^2 \sin^2(\theta)}{2g} \]

3. **Setting the Two Expressions Equal**:
To check the assertion, we set the expressions for range and height equal to each other:
\[ \frac{u^2 \sin(2\theta)}{g} = \frac{u^2 \sin^2(\theta)}{2g} \]

4. **Simplifying the Equation**:
Canceling \( u^2 \) and \( g \) from both sides (assuming \( u \) and \( g \) are not zero), we get:
\[ \sin(2\theta) = \frac{1}{2} \sin^2(\theta) \]

5. **Using the Double Angle Identity**:
Recall that \( \sin(2\theta) = 2 \sin(\theta) \cos(\theta) \). Substituting this into the equation gives:
\[ 2 \sin(\theta) \cos(\theta) = \frac{1}{2} \sin^2(\theta) \]

6. **Rearranging the Equation**:
Rearranging yields:
\[ 4 \cos(\theta) = \sin(\theta) \]
This can be rewritten as:
\[ \tan(\theta) = 4 \]

7. **Finding the Angle**:
Therefore, \( \theta = \tan^{-1}(4) \). This confirms that the assertion is correct.

8. **Understanding the Reason**:
The reason states that the maximum range of a projectile is directly proportional to the square of the velocity and inversely proportional to the acceleration due to gravity. The formula for the maximum range \( R \) is:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]
This shows that the range is indeed proportional to \( u^2 \) and inversely proportional to \( g \).

9. **Conclusion**:
Both the assertion and the reason are correct, but the reason does not directly explain why the horizontal range and maximum height are equal for the angle \( \tan^{-1}(4) \). Therefore, the assertion is true, and the reason is also true, but it is not the correct explanation for the assertion.

### Final Answer:
- Assertion: True
- Reason: True, but not a correct explanation of the assertion.