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. anit-parallel 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 1: Understand the Motion of a Projectile
A projectile follows a parabolic path under the influence of gravity. At any point in its trajectory, it has both velocity and acceleration.

### Step 2: Analyze the Velocity at the Top of the Trajectory
At the top of the trajectory, the projectile reaches its maximum height. Here, the vertical component of the velocity becomes zero, and the projectile only has a horizontal component of velocity. Therefore, the direction of the velocity at the top is horizontal.

### Step 3: Analyze the Acceleration at the Top of the Trajectory
The only force acting on the projectile (ignoring air resistance) is gravity, which acts vertically downward. Thus, the acceleration due to gravity is directed downward.

### Step 4: Determine the Relationship Between Velocity and Acceleration
Since the velocity at the top is horizontal and the acceleration due to gravity is vertical, the two vectors are at right angles to each other. This means they are perpendicular.

### Conclusion
Thus, at the top of the trajectory of a projectile, the directions of its velocity and acceleration are perpendicular to each other.

### Final Answer
The correct option is (a) perpendicular to each other.

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