A body of mass 2 kg is projected at 20 `ms^(-1)` at an angle `60^(@)`above the horizontal. Power due to the gravitational force at its highest point is

Options

A. 200 W
B. `100sqrt3` W
C. 50 W
D. zero

Explanation

To solve the problem of finding the power due to the gravitational force at the highest point of the projectile motion, we can follow these steps:

### Step 1: Understand the Motion
When a body is projected at an angle, it follows a parabolic path. At the highest point of its trajectory, the vertical component of its velocity becomes zero, while the horizontal component remains.

### Step 2: Calculate the Horizontal Component of Velocity
The initial velocity \( v_0 \) is given as \( 20 \, \text{ms}^{-1} \) and the angle of projection \( \theta \) is \( 60^\circ \).

The horizontal component of the velocity \( v_x \) can be calculated using the formula:
\[ v_x = v_0 \cdot \cos(\theta) \]
Substituting the values:
\[ v_x = 20 \cdot \cos(60^\circ) = 20 \cdot \frac{1}{2} = 10 \, \text{ms}^{-1} \]

### Step 3: Identify the Forces Acting on the Body
At the highest point, the only force acting on the body is the gravitational force \( F_g \), which is directed downwards. The gravitational force can be calculated as:
\[ F_g = m \cdot g \]
where \( m = 2 \, \text{kg} \) and \( g = 9.8 \, \text{ms}^{-2} \) (approximately).

Calculating the gravitational force:
\[ F_g = 2 \cdot 9.8 = 19.6 \, \text{N} \]

### Step 4: Determine the Angle Between Force and Velocity
At the highest point, the gravitational force acts vertically downwards, while the horizontal component of the velocity is horizontal. Therefore, the angle \( \phi \) between the gravitational force and the velocity vector is \( 90^\circ \).

### Step 5: Calculate the Power
Power \( P \) due to a force is given by the formula:
\[ P = \vec{F} \cdot \vec{v} \]
This can also be expressed as:
\[ P = F \cdot v \cdot \cos(\phi) \]
Since the angle \( \phi \) is \( 90^\circ \), we have:
\[ \cos(90^\circ) = 0 \]
Thus, the power becomes:
\[ P = F_g \cdot v_x \cdot \cos(90^\circ) = 19.6 \cdot 10 \cdot 0 = 0 \, \text{W} \]

### Conclusion
The power due to the gravitational force at the highest point is \( 0 \, \text{W} \).