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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 accelerationfor one instant only

D

is perpendicular to the acceleration for two instants

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The correct Answer is:
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**: - In projectile motion, an object is thrown into the air and moves under the influence of gravity. The motion can be broken down into horizontal and vertical components. 2. **Velocity in Projectile Motion**: - The velocity of the projectile can be described as having two components: horizontal (Vx) and vertical (Vy). The horizontal component remains constant (assuming no air resistance), while the vertical component changes due to gravitational acceleration. 3. **Acceleration in Projectile Motion**: - The only acceleration acting on the projectile is gravitational acceleration (g), which acts downwards towards the center of the Earth. This acceleration is constant and has a value of approximately 9.81 m/s². 4. **Analyzing the Relationship**: - At any point in the projectile's path, the velocity vector (which has both horizontal and vertical components) and the acceleration vector (which is always directed downwards) can be compared. - The angle between the velocity vector and the acceleration vector is crucial in understanding their relationship. 5. **Key Points**: - At the peak of the projectile's trajectory, the vertical component of the velocity (Vy) is zero, but the horizontal component (Vx) remains. However, the acceleration due to gravity is still acting downwards. - At this peak point, the velocity vector is horizontal, and the acceleration vector is vertical, making them perpendicular to each other. 6. **Conclusion**: - The only instance where the velocity and acceleration are perpendicular occurs at the highest point of the projectile's trajectory. Therefore, the correct answer to the question is that the velocity is perpendicular to the acceleration only at one specific instant (the peak of the trajectory). ### Final Answer: The velocity and acceleration in projectile motion are perpendicular to each other only at the peak of the trajectory. ---
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