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Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is?
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Two stones are thrown simultaneously from the same point with speed V ...
Stone 1 is thrown at an angle of . Therefore, the x-axis component of the velocity is
vcos(\theta) = vcos(30^{o}) = \frac{\sqrt{3} }{2}v.
Stone 2 is thrown at an angle of Therefore, the x-axis component of the velocity is
vcos(\theta) = vcos(60^{o}) = \frac{1 }{2}v.
Since the two stones move in the same direction, the relative velocity is the difference between the two velocities; which is
frac{\sqrt{3} }{2}v-\frac{1}{2}v = 0.366v
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Two stones are thrown simultaneously from the same point with speed V ...
Relative Velocity of Two Stones Thrown Simultaneously
Introduction:
When two stones are thrown simultaneously from the same point with different angles relative to the positive x-axis, we can determine the velocity with which they move relative to each other in the air.
Explanation:
To understand the relative velocity of the two stones, we need to break down their velocities into their x and y components.
Components of Velocity:
Stone 1 is thrown at an angle of 30 degrees with the positive x-axis, while Stone 2 is thrown at an angle of 60 degrees. The initial velocities of the stones can be represented as follows:
Stone 1: V₁x = V * cos(30°) and V₁y = V * sin(30°)
Stone 2: V₂x = V * cos(60°) and V₂y = V * sin(60°)
Relative Velocity:
The relative velocity of Stone 2 with respect to Stone 1 can be calculated by subtracting the x and y components of Stone 1 from the x and y components of Stone 2, respectively.
Relative Velocity (Vrel) = (V₂x - V₁x) î + (V₂y - V₁y) ĵ
Using the trigonometric identities cos(30°) = √3/2, sin(30°) = 1/2, cos(60°) = 1/2, and sin(60°) = √3/2, we can substitute the values into the equation:
Vrel = (V * (1/2) - V * (√3/2)) î + (V * (√3/2) - V * (1/2)) ĵ
Simplifying the equation further:
Vrel = (V/2 - (√3/2) * V) î + (√3/2 * V - V/2) ĵ
Vrel = (- (√3/2) * V) î + (√3/2 * V) ĵ
Conclusion:
Therefore, the relative velocity of the two stones in the air is given by Vrel = (- (√3/2) * V) î + (√3/2 * V) ĵ. This means that the stones move relative to each other at an angle of 60 degrees with the positive x-axis. The magnitude of the relative velocity is (√3/2) times the magnitude of the initial velocity V.
Introduction:
When two stones are thrown simultaneously from the same point with different angles relative to the positive x-axis, we can determine the velocity with which they move relative to each other in the air.
Explanation:
To understand the relative velocity of the two stones, we need to break down their velocities into their x and y components.
Components of Velocity:
Stone 1 is thrown at an angle of 30 degrees with the positive x-axis, while Stone 2 is thrown at an angle of 60 degrees. The initial velocities of the stones can be represented as follows:
Stone 1: V₁x = V * cos(30°) and V₁y = V * sin(30°)
Stone 2: V₂x = V * cos(60°) and V₂y = V * sin(60°)
Relative Velocity:
The relative velocity of Stone 2 with respect to Stone 1 can be calculated by subtracting the x and y components of Stone 1 from the x and y components of Stone 2, respectively.
Relative Velocity (Vrel) = (V₂x - V₁x) î + (V₂y - V₁y) ĵ
Using the trigonometric identities cos(30°) = √3/2, sin(30°) = 1/2, cos(60°) = 1/2, and sin(60°) = √3/2, we can substitute the values into the equation:
Vrel = (V * (1/2) - V * (√3/2)) î + (V * (√3/2) - V * (1/2)) ĵ
Simplifying the equation further:
Vrel = (V/2 - (√3/2) * V) î + (√3/2 * V - V/2) ĵ
Vrel = (- (√3/2) * V) î + (√3/2 * V) ĵ
Conclusion:
Therefore, the relative velocity of the two stones in the air is given by Vrel = (- (√3/2) * V) î + (√3/2 * V) ĵ. This means that the stones move relative to each other at an angle of 60 degrees with the positive x-axis. The magnitude of the relative velocity is (√3/2) times the magnitude of the initial velocity V.
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Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is?
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Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is?.
Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two stones are thrown simultaneously from the same point with speed V not at an angle 30degree and 60 degree respectively with the positive x-axis. the velocity with which stone move relative to each other in air is?.
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