A bode mass m is projected at an angle `theta` with the horizontal with an initial velocity u, the average power of gravitational force over the whole time of flight is.

Options

A. `mgu cos theta`
B. `1/2mgsqrt(u cos theta)`
C. `1/2mgu sin theta`
D. `zero`

Explanation

To solve the problem of finding the average power of the gravitational force over the whole time of flight for a body projected at an angle θ with an initial velocity u, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces Involved**:
- When a body is projected at an angle θ, it experiences gravitational force acting downwards. The gravitational force (weight) is given by \( F_g = mg \), where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

2. **Identify the Displacement**:
- The body moves in a projectile motion, which has both horizontal and vertical components. However, the work done by the gravitational force depends on the vertical displacement.

3. **Calculate Work Done by Gravitational Force**:
- The work done by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\phi) \]
where \( \phi \) is the angle between the force and the displacement.
- In this case, the gravitational force acts vertically downwards while the displacement during the entire time of flight has a horizontal component. Thus, the angle \( \phi \) between the gravitational force and the horizontal displacement is 90 degrees.
- Since \( \cos(90^\circ) = 0 \), the work done by the gravitational force is:
\[ W_g = mg \cdot d \cdot \cos(90^\circ) = 0 \]

4. **Calculate Average Power**:
- Average power is defined as the work done divided by the time taken:
\[ P_{avg} = \frac{W}{t} \]
- Since the work done \( W_g = 0 \), we substitute this into the average power formula:
\[ P_{avg} = \frac{0}{t} = 0 \]

5. **Conclusion**:
- Therefore, the average power of the gravitational force over the whole time of flight is \( 0 \).

### Final Answer:
The average power of the gravitational force over the whole time of flight is \( 0 \).

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