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Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella?
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Rain is falling vertically with the speed of 30 m/s. A man rides a bic...
Understanding the Situation
When it rains, the rain falls vertically downwards due to gravity. The man riding the bicycle is moving horizontally from east to west at a speed of 10 m/s. Therefore, the rain appears to come at an angle relative to him.
Relative Velocity of Rain
To find the direction in which the man should hold his umbrella, we need to consider the relative velocity of the rain with respect to the man.
Calculating the Resultant Velocity
The resultant velocity of the rain as perceived by the man can be determined by combining the vertical and horizontal components:
Using vector addition, we can visualize the resulting direction of the rain relative to the man.
Finding the Angle
The man needs to hold the umbrella in the direction of the resultant vector of these two components. This resultant vector will point diagonally backward (west) and downward.
Conclusion
To avoid getting wet, the man should hold the umbrella tilted backward at an angle such that it covers the direction from which the rain appears to be coming. This angle will be more than vertical but less than horizontal, ensuring effective coverage against the rain.
When it rains, the rain falls vertically downwards due to gravity. The man riding the bicycle is moving horizontally from east to west at a speed of 10 m/s. Therefore, the rain appears to come at an angle relative to him.
Relative Velocity of Rain
To find the direction in which the man should hold his umbrella, we need to consider the relative velocity of the rain with respect to the man.
- The rain is falling vertically at 30 m/s.
- The man is moving westward at 10 m/s.
Calculating the Resultant Velocity
The resultant velocity of the rain as perceived by the man can be determined by combining the vertical and horizontal components:
- Vertical component (rain): 30 m/s downward
- Horizontal component (bicycle): 10 m/s left (westward)
Using vector addition, we can visualize the resulting direction of the rain relative to the man.
Finding the Angle
The man needs to hold the umbrella in the direction of the resultant vector of these two components. This resultant vector will point diagonally backward (west) and downward.
- The angle of the umbrella can be calculated using basic trigonometry.
- However, intuitively, he should tilt the umbrella towards the point where the rain appears to be coming from, which is slightly back at an angle.
Conclusion
To avoid getting wet, the man should hold the umbrella tilted backward at an angle such that it covers the direction from which the rain appears to be coming. This angle will be more than vertical but less than horizontal, ensuring effective coverage against the rain.
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Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella?
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Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella?.
Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella?.
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