In a projectile motion the velocity

Options

A. is always perpendicular to the acceleration
B. is never perpendicular to the acceleration
C. is perpendicular to the acceleration for one instant only
D. is perpendicular to the acceleration for two instant

Explanation

To solve the question regarding the relationship between velocity and acceleration in projectile motion, we will analyze the motion step by step.

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- Projectile motion consists of two components: horizontal motion and vertical motion. The horizontal motion has a constant velocity (no acceleration), while the vertical motion is influenced by gravity, which acts downward with an acceleration of \( g \).

2. **Defining Velocity and Acceleration**:
- The velocity vector (\( \vec{v} \)) at any point in projectile motion is tangent to the trajectory of the projectile.
- The acceleration vector (\( \vec{a} \)) is constant and directed downward due to gravity.

3. **Analyzing the Direction of Velocity and Acceleration**:
- At any point during the projectile's flight, the velocity vector will have both horizontal (\( v_x \)) and vertical (\( v_y \)) components.
- The acceleration vector is always directed downward (negative y-direction).

4. **Conditions for Perpendicularity**:
- For two vectors to be perpendicular, the angle between them must be \( 90^\circ \).
- This condition occurs when the vertical component of the velocity (\( v_y \)) is zero, meaning the projectile is at its highest point.

5. **Identifying the Instant of Perpendicularity**:
- At the highest point of the projectile's trajectory:
- The vertical component of velocity (\( v_y \)) becomes zero.
- The horizontal component (\( v_x \)) remains non-zero.
- Thus, at this instant, the velocity vector is horizontal, while the acceleration vector is vertical, making them perpendicular.

6. **Conclusion**:
- The velocity is perpendicular to the acceleration only at the highest point of the projectile's path and at the initial moment of a horizontal projection.
- Therefore, the correct answer is that the velocity is perpendicular to the acceleration for one instant only.

### Final Answer:
The correct option is **C: Perpendicular to the acceleration for one instant only**.