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At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is?
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At a height of 0.4m from the ground the velocity of a projectile in ve...
Understanding the Projectile Motion
To determine the angle of projection from the horizontal, we can analyze the velocity vector of the projectile given as v = (6i + 2j) m/s.
Components of Velocity
- Horizontal Component (vx): 6 m/s
- Vertical Component (vy): 2 m/s
Calculating the Angle of Projection
The angle of projection (θ) can be found using the tangent function, which relates the vertical and horizontal components of the velocity.
- Formula: tan(θ) = vy / vx
Here, substituting the values:
- tan(θ) = 2 / 6 = 1/3
Finding the Angle
To find the angle θ, we take the arctangent (inverse tangent) of 1/3:
- θ = arctan(1/3)
This gives us the angle of projection from the horizontal.
Calculation Result
Using a calculator or tables, we find:
- θ ≈ 18.43 degrees
Conclusion
The angle of projection from the horizontal for the given projectile at a height of 0.4m is approximately 18.43 degrees. This angle is crucial for understanding the trajectory and range of the projectile in motion.
To determine the angle of projection from the horizontal, we can analyze the velocity vector of the projectile given as v = (6i + 2j) m/s.
Components of Velocity
- Horizontal Component (vx): 6 m/s
- Vertical Component (vy): 2 m/s
Calculating the Angle of Projection
The angle of projection (θ) can be found using the tangent function, which relates the vertical and horizontal components of the velocity.
- Formula: tan(θ) = vy / vx
Here, substituting the values:
- tan(θ) = 2 / 6 = 1/3
Finding the Angle
To find the angle θ, we take the arctangent (inverse tangent) of 1/3:
- θ = arctan(1/3)
This gives us the angle of projection from the horizontal.
Calculation Result
Using a calculator or tables, we find:
- θ ≈ 18.43 degrees
Conclusion
The angle of projection from the horizontal for the given projectile at a height of 0.4m is approximately 18.43 degrees. This angle is crucial for understanding the trajectory and range of the projectile in motion.
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At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is?
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At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is?.
At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a height of 0.4m from the ground the velocity of a projectile in vector form is v=(6î+2j)m/s, the angle of projection from horizontal is?.
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