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Assertion: In projectile motion horizont...

Assertion: In projectile motion horizontal velocity remains same but vertical velocity continously change Reason: particle strikes the ground with same vertical velocity with which the particle was thrwon in vertical direction.

A

If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.

B

If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.

C

If Assertion is Trie but the Reason is False.

D

If both Assertion `&` Reason are false

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the assertion and reason provided in the question, we will break down the concepts of projectile motion step by step. ### Step 1: Understanding Projectile Motion In projectile motion, an object is launched into the air and moves under the influence of gravity. The motion can be analyzed in two dimensions: horizontal (x-direction) and vertical (y-direction). **Hint:** Remember that projectile motion can be divided into horizontal and vertical components. ### Step 2: Horizontal Motion In the horizontal direction, there are no external forces acting on the projectile (assuming air resistance is negligible). Therefore, the horizontal velocity remains constant throughout the motion. **Hint:** Think about Newton's first law of motion: an object in motion stays in motion unless acted upon by an external force. ### Step 3: Vertical Motion In contrast, the vertical motion is influenced by gravity. The force acting on the projectile is its weight (mg), which causes a downward acceleration (g). This means that the vertical component of velocity changes continuously as the projectile moves upward and then downward. **Hint:** Recall that the vertical motion is affected by gravitational acceleration, which changes the vertical velocity over time. ### Step 4: Energy Conservation in Vertical Motion The total mechanical energy in the vertical direction is conserved. At the highest point of the projectile's trajectory, the vertical velocity is zero, and all the energy is kinetic. As the projectile falls back down, it converts potential energy back into kinetic energy. **Hint:** Use the principle of conservation of energy to relate initial and final energies in vertical motion. ### Step 5: Final Vertical Velocity When the projectile strikes the ground, its vertical velocity will be equal in magnitude but opposite in direction to the initial vertical velocity (ignoring air resistance). This means that the vertical velocity when it hits the ground is the same as the initial vertical velocity. **Hint:** Think about how the projectile's vertical motion is symmetrical; it will have the same speed when returning to the original launch height. ### Step 6: Evaluating the Assertion and Reason - **Assertion:** True. The horizontal velocity remains constant while the vertical velocity changes. - **Reason:** True. The particle strikes the ground with the same vertical velocity with which it was thrown. However, the reason provided does not correctly explain the assertion. The assertion is based on the absence of horizontal forces, while the reason focuses on energy conservation. **Hint:** Distinguish between the cause of the assertion and the explanation provided by the reason. ### Conclusion Both the assertion and reason are true, but the reason is not the correct explanation for the assertion. ### Final Summary - **Assertion:** True - Horizontal velocity remains constant; vertical velocity changes. - **Reason:** True - Particle strikes the ground with the same vertical velocity as it was thrown. - **Conclusion:** The reason does not explain the assertion correctly.
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