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In a projectile motion the velocity...

In a projectile motion the velocity

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 instants

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To determine the relationship between velocity and acceleration in projectile motion, we can analyze the motion step by step. ### Step-by-Step Solution: 1. **Understanding Projectile Motion**: - In projectile motion, an object is thrown into the air and moves under the influence of gravity. The motion can be analyzed in two dimensions: horizontal and vertical. 2. **Identifying Velocity and Acceleration**: - The velocity of the projectile is always tangent to the path of the projectile. This means that at any point in the trajectory, the velocity vector points in the direction of motion. - The acceleration due to gravity acts vertically downward with a constant magnitude of \( g \). 3. **Analyzing Different Points in the Trajectory**: - Let's consider three key points in the projectile's path: - Point A (at the launch point) - Point F (at the peak of the trajectory) - Point G (on the way down) 4. **At Point A**: - At the launch point A, the projectile has a horizontal velocity component and no vertical component. The acceleration due to gravity acts downward. - Here, the angle between the velocity and acceleration is \( 90^\circ \). 5. **At Point F (the highest point)**: - At point F, the vertical component of the velocity is zero, and the projectile has only horizontal velocity. The acceleration is still acting downward. - The angle between the velocity and acceleration is \( 90^\circ \). 6. **At Point G (on the way down)**: - As the projectile descends, it has both horizontal and vertical components of velocity. The vertical component is increasing due to acceleration from gravity. - The angle between the velocity and acceleration is less than \( 90^\circ \) as the projectile moves downward. 7. **Conclusion**: - Throughout the projectile's path, the velocity and acceleration are perpendicular only at the launch point A and at the peak point F. Thus, there are two instances where the velocity is perpendicular to the acceleration. ### Final Answer: The velocity in projectile motion is perpendicular to the acceleration for two instants.
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