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

Options

A. (a)parallel to each other
B. (b)anti-parallel to each other
C. (c)inclined to each other at an angle of `45^@`
D. (d)perpendicular to each other

Explanation

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. **Understand the Motion of a Projectile**:
A projectile is an object that is thrown into the air with an initial velocity and is subject to gravitational acceleration. The motion can be analyzed in two dimensions: horizontal (x-axis) and vertical (y-axis).

2. **Identify the Trajectory**:
The trajectory of a projectile is a parabolic path. At the peak (top) of this trajectory, the vertical component of the velocity becomes zero.

3. **Analyze Velocity at the Top of the Trajectory**:
At the top of the trajectory, the projectile has only horizontal velocity. The vertical component of the velocity (Vy) is zero, while the horizontal component (Vx) remains constant.

4. **Analyze Acceleration at the Top of the Trajectory**:
The only acceleration acting on the projectile is due to gravity, which acts downward (toward the Earth). This acceleration is constant and has a magnitude of 'g'.

5. **Determine the Directions**:
- The direction of the velocity at the top of the trajectory is horizontal (along the x-axis).
- The direction of the acceleration due to gravity is vertical (downward along the y-axis).

6. **Conclusion**:
Since the velocity is horizontal and the acceleration due to gravity is vertical, they are perpendicular to each other at the top of the trajectory.

### Final Answer:
At the top of the trajectory of a projectile, the directions of its velocity and acceleration are perpendicular to each other.

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