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A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-?
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A particle is projected from point O with velocity u in a direction ma...
**Projectile Motion**
Projectile motion refers to the motion of an object that is launched into the air and moves along a curved path under the influence of gravity. When a particle is projected from point O with velocity u at an angle α with the horizontal, it follows a parabolic path.
**Components of Velocity**
The initial velocity u can be resolved into two components: one along the horizontal direction (uₓ) and the other along the vertical direction (uᵧ). The horizontal component remains constant throughout the motion, while the vertical component changes due to the influence of gravity.
The vertical component of velocity (uᵧ) can be calculated using the equation:
uᵧ = u * sin(α)
The horizontal component of velocity (uₓ) can be calculated using the equation:
uₓ = u * cos(α)
**Position at Point P**
At any instant, the position of the particle is at point P, which is at right angles to the initial direction of projection. This means that the particle has reached its maximum height and is about to descend. Point P is located on the parabolic path of the projectile.
**Velocity at Point P**
The velocity at point P can be determined by considering the change in vertical and horizontal components of the velocity.
1. Vertical Component of Velocity at Point P:
At point P, the vertical component of velocity becomes zero as the particle reaches its maximum height and starts descending. This is because the particle has momentarily come to a stop in the vertical direction before changing direction and accelerating downwards. Therefore, the vertical component of velocity at point P is zero (vᵧ = 0).
2. Horizontal Component of Velocity at Point P:
The horizontal component of velocity remains constant throughout the motion and does not change at point P. Therefore, the horizontal component of velocity at point P is the same as the initial horizontal component (uₓ).
Hence, the velocity at point P is given by:
v = √(vₓ² + vᵧ²) = √(uₓ² + vᵧ²) = √(uₓ² + 0) = uₓ
Therefore, the velocity at point P is equal to the horizontal component of the initial velocity (uₓ).
Projectile motion refers to the motion of an object that is launched into the air and moves along a curved path under the influence of gravity. When a particle is projected from point O with velocity u at an angle α with the horizontal, it follows a parabolic path.
**Components of Velocity**
The initial velocity u can be resolved into two components: one along the horizontal direction (uₓ) and the other along the vertical direction (uᵧ). The horizontal component remains constant throughout the motion, while the vertical component changes due to the influence of gravity.
The vertical component of velocity (uᵧ) can be calculated using the equation:
uᵧ = u * sin(α)
The horizontal component of velocity (uₓ) can be calculated using the equation:
uₓ = u * cos(α)
**Position at Point P**
At any instant, the position of the particle is at point P, which is at right angles to the initial direction of projection. This means that the particle has reached its maximum height and is about to descend. Point P is located on the parabolic path of the projectile.
**Velocity at Point P**
The velocity at point P can be determined by considering the change in vertical and horizontal components of the velocity.
1. Vertical Component of Velocity at Point P:
At point P, the vertical component of velocity becomes zero as the particle reaches its maximum height and starts descending. This is because the particle has momentarily come to a stop in the vertical direction before changing direction and accelerating downwards. Therefore, the vertical component of velocity at point P is zero (vᵧ = 0).
2. Horizontal Component of Velocity at Point P:
The horizontal component of velocity remains constant throughout the motion and does not change at point P. Therefore, the horizontal component of velocity at point P is the same as the initial horizontal component (uₓ).
Hence, the velocity at point P is given by:
v = √(vₓ² + vᵧ²) = √(uₓ² + vᵧ²) = √(uₓ² + 0) = uₓ
Therefore, the velocity at point P is equal to the horizontal component of the initial velocity (uₓ).
Community Answer
A particle is projected from point O with velocity u in a direction ma...
U making an angle aloha with horizontal in downward direction
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A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-?
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A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-?.
A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected from point O with velocity u in a direction making an angle alpha with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is-?.
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