A body is projected from ground obliquely. During downward motion, power delivered by gravity of it

Options

A. Increases
B. decreases
C. Remains constant
D. First decreases and then becomes constant

Answer

To solve the problem of determining the power delivered by gravity during the downward motion of a body projected obliquely, we can follow these steps:

### Step 1: Understand the Concept of Power
Power is defined as the rate at which work is done. Mathematically, it can be expressed as:
\[ P = \frac{W}{t} \]
where \( P \) is power, \( W \) is work done, and \( t \) is the time taken.

### Step 2: Relate Work Done to Force and Displacement
The work done by a force can be expressed as:
\[ W = F \cdot s \]
where \( F \) is the force acting on the body and \( s \) is the displacement of the body in the direction of the force.

### Step 3: Express Power in Terms of Force and Velocity
Since power is also the product of force and velocity, we can write:
\[ P = F \cdot v \]
where \( v \) is the velocity of the body.

### Step 4: Identify the Force Acting on the Body
In this case, the force acting on the body is the gravitational force, which acts downward. The gravitational force \( F \) can be given by:
\[ F = mg \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

### Step 5: Analyze the Direction of Force and Velocity
During the downward motion, the direction of the gravitational force \( F \) and the velocity \( v \) of the body are both directed downward. Therefore, the angle \( \theta \) between the force and the velocity is 0 degrees.

### Step 6: Calculate the Power Delivered by Gravity
Since the angle between the force and the velocity is 0 degrees, we can express the power as:
\[ P = F \cdot v \cdot \cos(0) = F \cdot v \]
Substituting the expression for gravitational force:
\[ P = mg \cdot v \]

### Step 7: Conclusion
Since both \( mg \) and \( v \) are positive quantities, the power delivered by gravity during the downward motion is positive, which indicates that the power is increasing as the body falls.

### Final Answer
The power delivered by gravity during the downward motion of the body is positive and increases.

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