Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: When a body is projected at an angle `45,^@` it’s range is maximum .
Reason R: For maximum range, the value of sin `2theta` should be equal to one
In the light of the above statements, choose the correct answer from the options given below:

Options

A. A is false but R is true
B. A is true but R is false
C. Both A and R are correct and R is the correct explanation of A
D. Both A and R are correct but R is NOT the correct explanation of A

Answer

To solve the problem, we need to analyze the two statements provided: Assertion A and Reason R.

### Step 1: Understanding the Assertion A
Assertion A states that "When a body is projected at an angle of 45 degrees, its range is maximum."

To verify this, we can use the formula for the range \( R \) of a projectile, which is given by:
\[ R = \frac{u^2 \sin 2\theta}{g} \]
where:
- \( u \) is the initial velocity,
- \( g \) is the acceleration due to gravity,
- \( \theta \) is the angle of projection.

### Step 2: Finding the Maximum Range
To find the angle that gives the maximum range, we need to maximize \( \sin 2\theta \). The maximum value of \( \sin 2\theta \) is 1, which occurs when \( 2\theta = 90^\circ \) or \( \theta = 45^\circ \).

Thus, when the angle of projection is \( 45^\circ \), the range is indeed maximum.

### Step 3: Understanding the Reason R
Reason R states that "For maximum range, the value of \( \sin 2\theta \) should be equal to one."

From our previous analysis, we found that for maximum range, \( \sin 2\theta \) must equal 1, which occurs at \( \theta = 45^\circ \). Therefore, this statement is also correct.

### Conclusion
Both Assertion A and Reason R are correct, and Reason R provides the correct explanation for Assertion A.

### Final Answer
Both Assertion A and Reason R are correct, and R is the correct explanation for A.