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Assertion At highest point of a projecti...

Assertion At highest point of a projectile, dot product of velocity and acceleration is zero.
Reason At highest point, velocity and acceleration are mutually perpendicular.

A

If both Asseration and Reason are correct and Reason is the correct explanation of Assertion

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion

C

If Assertion is true but Reason is false

D

If Assertion is false but Reason is true

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Motion of a Projectile**: - When a projectile is thrown upwards, it moves along a parabolic path. The highest point of this trajectory is known as the apex. 2. **Velocity at the Highest Point**: - At the highest point, the vertical component of the projectile's velocity becomes zero. However, if the projectile is thrown at an angle, it still has a horizontal component of velocity. 3. **Acceleration Due to Gravity**: - The only force acting on the projectile (after it has been thrown) is the force of gravity, which acts downwards with an acceleration of \( g \) (approximately \( 9.81 \, m/s^2 \)). 4. **Direction of Velocity and Acceleration**: - At the highest point, the direction of the velocity vector is horizontal (if we consider the projectile was thrown at an angle), while the acceleration vector (due to gravity) is vertical and directed downwards. 5. **Dot Product of Velocity and Acceleration**: - The dot product of two vectors \( \vec{A} \) and \( \vec{B} \) is given by: \[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos(\theta) \] where \( \theta \) is the angle between the two vectors. - At the highest point, the angle \( \theta \) between the velocity vector (horizontal) and the acceleration vector (vertical) is \( 90^\circ \). - Thus, the dot product becomes: \[ \vec{v} \cdot \vec{a} = |\vec{v}| |\vec{a}| \cos(90^\circ) = 0 \] - Therefore, the assertion that the dot product of velocity and acceleration is zero is correct. 6. **Mutual Perpendicularity**: - Since the velocity vector is horizontal and the acceleration vector is vertical at the highest point, they are indeed mutually perpendicular. This confirms the reason provided is also correct. 7. **Conclusion**: - Both the assertion and the reason are correct, and the reason correctly explains the assertion. ### Final Answer: - Both the assertion and the reason are correct, and the reason is the correct explanation of the assertion.

To solve the question, we need to analyze the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Motion of a Projectile**: - When a projectile is thrown upwards, it moves along a parabolic path. The highest point of this trajectory is known as the apex. 2. **Velocity at the Highest Point**: ...
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