STATEMENT-1: A body is projected from the ground with kinetic energy K at an angle of 60° with the horizontal. If air resistance is neglected, its K.E. When it is at the highest point of its trajectory will be K/4
because
STATEMENT-2: At the highest point of the trajectory, the direction of velocity and acceleration of the body are perpendicular to each other

Options

A. Statement-1 is True, Statement-2 is True, Statement -2 is a correct explanation for
Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement -2 is NOT a correct explanation for
Statement-1
C. Statement - 1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

To solve the problem, we need to analyze the two statements provided regarding the motion of a projectile.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- A body is projected with an initial kinetic energy \( K \) at an angle of \( 60^\circ \) with the horizontal.
- The initial velocity \( u \) can be related to the kinetic energy using the formula:
\[ K = \frac{1}{2} m u^2 \]
- From this, we can express the initial velocity as:
\[ u = \sqrt{\frac{2K}{m}} \]

2. **Components of the Initial Velocity**:
- The initial velocity can be broken down into horizontal and vertical components:
- Horizontal component: \( u_x = u \cos(60^\circ) = u \cdot \frac{1}{2} = \frac{u}{2} \)
- Vertical component: \( u_y = u \sin(60^\circ) = u \cdot \frac{\sqrt{3}}{2} \)

3. **Velocity at the Highest Point**:
- At the highest point of the trajectory, the vertical component of the velocity becomes zero (\( v_y = 0 \)), and only the horizontal component remains:
\[ v = u_x = \frac{u}{2} \]

4. **Kinetic Energy at the Highest Point**:
- The kinetic energy at the highest point can be calculated using the remaining horizontal component of the velocity:
\[ K' = \frac{1}{2} m v^2 = \frac{1}{2} m \left(\frac{u}{2}\right)^2 = \frac{1}{2} m \cdot \frac{u^2}{4} = \frac{1}{4} \cdot \frac{1}{2} m u^2 = \frac{K}{4} \]
- Therefore, the kinetic energy at the highest point is indeed \( \frac{K}{4} \).

5. **Direction of Velocity and Acceleration**:
- At the highest point, the direction of the velocity is horizontal (along the x-axis), while the acceleration due to gravity acts vertically downward (along the y-axis).
- Since these two directions are perpendicular to each other, this confirms that statement 2 is true.

### Conclusion:
- Both statements are true:
- **Statement 1**: The kinetic energy at the highest point is \( \frac{K}{4} \).
- **Statement 2**: The direction of velocity and acceleration are perpendicular at the highest point.
- However, statement 2 does not provide the correct explanation for statement 1.

### Final Answer:
- Both statements are true, but statement 2 is not the correct explanation for statement 1. Thus, the answer is (B).