(A): The path followed by one projectile as observed by another projectile is a straight line in uniform gravitation field.
(R): The relative velocity between two projectiles at a given place doesn't change with time. Because their relative acceleration is zero.

Options

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

Answer

To solve the question, we will analyze the statements (A) and (R) and determine their validity based on the principles of projectile motion in a uniform gravitational field.

### Step-by-Step Solution:

1. **Understanding the Motion of Projectiles**:
- When two projectiles are launched, they follow a parabolic trajectory due to the influence of gravity.
- However, when we observe one projectile from the perspective of another, we need to consider their relative motion.

2. **Relative Motion in a Uniform Gravitational Field**:
- In a uniform gravitational field, the acceleration due to gravity (g) acts equally on both projectiles.
- The key point here is that both projectiles experience the same gravitational acceleration downward.

3. **Relative Velocity**:
- The relative velocity of one projectile with respect to another can be expressed as:
\[ \text{Relative Velocity} = \text{Velocity of Projectile 1} - \text{Velocity of Projectile 2} \]
- Since both projectiles are subject to the same gravitational acceleration, their velocities will change in the same manner over time.

4. **Relative Acceleration**:
- The relative acceleration between the two projectiles is given by:
\[ \text{Relative Acceleration} = \text{Acceleration of Projectile 1} - \text{Acceleration of Projectile 2} \]
- Since both projectiles have the same acceleration (g downward), the relative acceleration is zero:
\[ \text{Relative Acceleration} = g - g = 0 \]

5. **Conclusion about the Path**:
- Because the relative acceleration is zero, the relative velocity remains constant over time.
- This means that the path followed by one projectile as observed by the other will be a straight line.

6. **Validity of Statements**:
- (A): The path followed by one projectile as observed by another projectile is a straight line in a uniform gravitational field. **(True)**
- (R): The relative velocity between two projectiles at a given place doesn't change with time because their relative acceleration is zero. **(True)**

### Final Answer:
Both statements (A) and (R) are true, and (R) correctly explains (A).

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