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A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be?
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A man is walking due to eat @ 4 km per hour and the rain is falling ve...
Understanding the Scenario
To find the velocity of rain relative to the man, we need to consider both the speed of the man and the speed of the rain.
Components of Motion
- Man’s Velocity: Walking at 4 km/h horizontally.
- Rain’s Velocity: Falling vertically at 6 km/h.
Relative Velocity Calculation
To calculate the velocity of the rain relative to the man, we can use vector addition. The man is moving in a horizontal direction while the rain is falling vertically.
Using the Pythagorean Theorem
1. Horizontal Component: 4 km/h (man’s speed).
2. Vertical Component: 6 km/h (rain’s speed).
3. Resultant Velocity:
Resultant velocity (V) can be calculated using:
V = √(horizontal² + vertical²)
Here,
- Horizontal = 4 km/h
- Vertical = 6 km/h
Final Calculation
- V = √(4² + 6²)
- V = √(16 + 36)
- V = √52
- V ≈ 7.21 km/h
Direction of the Rain's Velocity
- The direction can be found using the tangent function:
- θ = tan⁻¹(vertical/horizontal)
- θ = tan⁻¹(6/4)
This angle indicates how the rain is perceived by the man.
Conclusion
- Velocity of Rain Relative to Man: Approximately 7.21 km/h at an angle downwards towards the man, combining both horizontal and vertical motions.
This understanding helps in grasping relative motion in different frames of reference.
To find the velocity of rain relative to the man, we need to consider both the speed of the man and the speed of the rain.
Components of Motion
- Man’s Velocity: Walking at 4 km/h horizontally.
- Rain’s Velocity: Falling vertically at 6 km/h.
Relative Velocity Calculation
To calculate the velocity of the rain relative to the man, we can use vector addition. The man is moving in a horizontal direction while the rain is falling vertically.
Using the Pythagorean Theorem
1. Horizontal Component: 4 km/h (man’s speed).
2. Vertical Component: 6 km/h (rain’s speed).
3. Resultant Velocity:
Resultant velocity (V) can be calculated using:
V = √(horizontal² + vertical²)
Here,
- Horizontal = 4 km/h
- Vertical = 6 km/h
Final Calculation
- V = √(4² + 6²)
- V = √(16 + 36)
- V = √52
- V ≈ 7.21 km/h
Direction of the Rain's Velocity
- The direction can be found using the tangent function:
- θ = tan⁻¹(vertical/horizontal)
- θ = tan⁻¹(6/4)
This angle indicates how the rain is perceived by the man.
Conclusion
- Velocity of Rain Relative to Man: Approximately 7.21 km/h at an angle downwards towards the man, combining both horizontal and vertical motions.
This understanding helps in grasping relative motion in different frames of reference.
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A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be?
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A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be?.
A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is walking due to eat @ 4 km per hour and the rain is falling vertically drawn at the rate of 6 km per hour the velocity of rain relative to the man will be?.
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