The question given below consist of an assertion and the reason . Use the following key to choose appropriate answer:
Assertion : When path of one projectile is observed with respect to another projectile, then it is a straight line .
Reason : Both the projectiles are moving with the same acceleration , hence acceleration of one with respect to the other is zero .

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion
B. If both assertion and reason are correct but reason is not the correct explanation of assertion .
C. If assertion is correct but reason is incorrect .
(d) If assertion is incorrect but reason is correct .
D. If assertion is incorrect but reason is correct

Answer

To solve the assertion and reason question, we need to analyze both statements carefully.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that when the path of one projectile is observed with respect to another projectile, it appears as a straight line. This implies that the relative motion between the two projectiles must result in a linear trajectory.

2. **Understanding the Reason**:
- The reason provided states that both projectiles are moving with the same acceleration. Since they are both subject to the same gravitational force, their accelerations are equal. This means that the acceleration of one projectile with respect to the other is zero.

3. **Analyzing the Motion**:
- Let's denote the two projectiles as A and B. If both projectiles are launched with different initial velocities and angles, they will follow their respective parabolic paths under the influence of gravity.
- However, since they share the same gravitational acceleration (downward), the relative acceleration between them is zero.

4. **Relative Motion**:
- The relative velocity of projectile A with respect to B can be expressed as:
\[ \text{Velocity of A with respect to B} = \text{Velocity of A} - \text{Velocity of B} \]
- Since both projectiles have the same acceleration, the vertical components of their velocities will change at the same rate due to gravity. Thus, the vertical components of their relative velocities will cancel out.

5. **Conclusion**:
- Since the relative acceleration is zero, the path traced by one projectile with respect to the other will indeed be a straight line. Therefore, both the assertion and the reason are correct, and the reason correctly explains the assertion.

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

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