At the top of the trajectory of a projectile, the directions of its velocity and acceleration are

Options

A. Perpendicular to each other
B. Parallel to each other
C. Inclined to each other at an angle of `45^(@)`
D. Antiparallel to each other

Answer

To solve the question regarding the directions of velocity and acceleration at the top of the trajectory of a projectile, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- A projectile is an object that is thrown into the air with an initial velocity and is subject to the force of gravity. The motion can be analyzed in two dimensions: horizontal and vertical.

2. **Identifying the Top of the Trajectory**:
- At the top of the trajectory, the projectile reaches its maximum height. This is the point where the vertical component of its velocity becomes zero.

3. **Velocity at the Top**:
- At the peak, the projectile has only horizontal velocity. The vertical component of the velocity is zero because it has stopped rising and is about to start descending.

4. **Acceleration at the Top**:
- The only force acting on the projectile is gravity, which acts downward. Therefore, the acceleration due to gravity (denoted as \( g \)) is directed vertically downward.

5. **Direction of Velocity and Acceleration**:
- The velocity at the top of the trajectory is horizontal, while the acceleration due to gravity is vertical (downward).

6. **Angle Between Velocity and Acceleration**:
- Since the velocity is horizontal and the acceleration is vertical, the angle between them is 90 degrees.

### Conclusion:
- At the top of the trajectory of a projectile, the direction of its velocity is horizontal, and the direction of its acceleration is downward. Therefore, the angle between the velocity and acceleration is 90 degrees.