For a body projected at an angle with the horizontal from the ground, choose the correct statement :

Options

A. The kinetic energy (K.E.) is zero at the highest point of projectile motion.
B. The horizontal component of velocity is zero at the highest point
C. The vertical component of momentum is maximum at the highest point.
D. Gravitational potential energy is maximum at the highest point

Answer

To solve the problem, we need to analyze the motion of a body projected at an angle with respect to the horizontal. We will consider the components of motion and the energy transformations that occur during the projectile's flight.

### Step-by-Step Solution:

1. **Understanding the Components of Motion**:
- When a body is projected at an angle θ with the horizontal, its initial velocity (u) can be broken down into two components:
- Horizontal component: \( u_x = u \cos \theta \)
- Vertical component: \( u_y = u \sin \theta \)

2. **Maximum Height**:
- At the maximum height of the projectile's trajectory, the vertical component of the velocity becomes zero. Therefore, we have:
- \( v_y = 0 \) at maximum height.
- The horizontal component of the velocity remains unchanged throughout the motion (assuming no air resistance):
- \( v_x = u \cos \theta \)

3. **Kinetic Energy at Maximum Height**:
- The kinetic energy (KE) at any point is given by:
\[ KE = \frac{1}{2} m v^2 \]
- At maximum height, the kinetic energy can be calculated using the horizontal component:
\[ KE_{max\ height} = \frac{1}{2} m (u \cos \theta)^2 \]

4. **Potential Energy at Maximum Height**:
- The potential energy (PE) at maximum height is given by:
\[ PE = mgh_{max} \]
- Here, \( h_{max} \) is the maximum height reached by the projectile.

5. **Energy Conservation**:
- At the maximum height, the total mechanical energy is conserved. Thus, the potential energy will be maximum, and the kinetic energy due to the vertical motion will be zero.

6. **Correct Statement**:
- From the analysis, we can conclude the following:
- The horizontal component of the velocity is not zero at the highest point; it remains \( u \cos \theta \).
- The vertical component of the velocity is zero at the highest point.
- The gravitational potential energy is maximum at the highest point.
- The kinetic energy is not zero at the highest point; it is equal to the kinetic energy associated with the horizontal motion.

### Conclusion:
Based on the analysis, the correct statement is that the gravitational potential energy is maximum at the highest point of the projectile's motion.