In the following questions a statement of assertion (A) is followed by a statement of reason ( R).
A: Horizontal range of a projectile is always same for angle of projection `theta` with horizontal or `theta` with vertical .
R : Horizontal range depends only on angle of projection .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1) .
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion then mark (2)
C. If Assertion is true statement but Reason is false then mark (3).
D. If both Assertion and Reason are false statements then mark (4) .

Answer

To solve the problem, we will analyze both the assertion (A) and the reason (R) provided in the question.

### Step 1: Understanding the Assertion (A)

The assertion states that "the horizontal range of a projectile is always the same for an angle of projection θ with the horizontal or θ with the vertical."

**Analysis**:
- When a projectile is launched at an angle θ with the horizontal, the horizontal range (R) can be calculated using the formula:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]
where \( u \) is the initial velocity and \( g \) is the acceleration due to gravity.

- If the projectile is launched at an angle θ with the vertical, the angle with the horizontal becomes \( 90^\circ - \theta \). The range can be calculated as:
\[ R' = \frac{u^2 \sin(2(90^\circ - \theta))}{g} = \frac{u^2 \sin(180^\circ - 2\theta)}{g} = \frac{u^2 \sin(2\theta)}{g} \]

- Therefore, the horizontal range is the same for both angles of projection, which makes the assertion true.

### Step 2: Understanding the Reason (R)

The reason states that "the horizontal range depends only on the angle of projection."

**Analysis**:
- The horizontal range does depend on the angle of projection, but it also depends on the initial velocity of the projectile. The formula for range shows that both the angle and the initial velocity are factors:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]

- Since the range depends on both the angle of projection and the initial velocity, the reason is false.

### Conclusion

- The assertion (A) is **true**: the horizontal range is the same for angles θ with horizontal and vertical.
- The reason (R) is **false**: the range depends on both the angle of projection and the initial velocity.

### Final Answer

Both assertion and reason are not true together, so the correct answer is that the assertion is true, but the reason is false.

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