These questions consists of two statements each printed as Assertion and Reason. While answering these question you are required to choose any one of the following five reponses
(a) If both Assertion and Reason arecorrect and Reason is the correct explanation of Asserrtion.
(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.
Assertion At any instant the magnitude of rate of change of potential energy of the projectile of mass 1 kg is numerically equal to magnitude of a.v (where a is acceleration due to gravity and v is velocity at that instant)
Reason The graph representing power delivered by the gravitational force acting on the projectile with time will be straight line with negative slope.

Explanation

To solve the question, we will analyze the Assertion and Reason step by step.

### Step 1: Analyze the Assertion
The assertion states that "At any instant, the magnitude of the rate of change of potential energy of the projectile of mass 1 kg is numerically equal to the magnitude of \( a \cdot v \) (where \( a \) is acceleration due to gravity and \( v \) is velocity at that instant)."

1. The potential energy \( U \) of the projectile at height \( h \) is given by:
\[ U = mgh \]
where \( m = 1 \, \text{kg} \) and \( g \) is the acceleration due to gravity.

2. The rate of change of potential energy with respect to time is:
\[ \frac{dU}{dt} = \frac{d(mgh)}{dt} = mg \frac{dh}{dt} \]
Here, \( \frac{dh}{dt} \) is the vertical component of the velocity, denoted as \( v_y \).

3. Thus, we can write:
\[ \frac{dU}{dt} = mg v_y \]
Since \( m = 1 \, \text{kg} \), this simplifies to:
\[ \frac{dU}{dt} = g v_y \]

### Step 2: Analyze the Reason
The reason states that "The graph representing power delivered by the gravitational force acting on the projectile with time will be a straight line with a negative slope."

1. The power \( P \) delivered by the gravitational force is given by:
\[ P = F \cdot v \]
where \( F \) is the gravitational force \( mg \) and \( v \) is the velocity vector.

2. Since the gravitational force acts downward, the power can be expressed as:
\[ P = -mg v_y \]
where \( v_y \) is the vertical component of the velocity.

3. As the projectile moves upward, \( v_y \) decreases until it reaches the maximum height, where it becomes zero, and then it increases again as the projectile falls back down. Thus, the power \( P \) will not be a straight line with a negative slope; it will vary depending on the motion of the projectile.

### Conclusion
- The assertion is correct because the rate of change of potential energy is indeed equal to \( g v_y \).
- The reason is incorrect because the power graph does not represent a straight line with a negative slope; it varies with time.

### Final Answer
Based on the analysis:
- **Assertion is true**.
- **Reason is false**.

Thus, the correct response is:
**(c) If Assertion is true but Reason is false.**