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Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain?
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Rain is falling vertically with a speed of 25m/s.A cyclist is going at...
Explanation:
When rain falls vertically, its speed is equal to the speed of gravity, which is 9.8m/s^2.
Apparent Speed:
The apparent speed of rain as seen by the cyclist is the vector sum of the speed of rain and the speed of the cyclist.
Direction of Rain:
The direction of rain as seen by the cyclist is the direction of the vector sum of the speed of rain and the speed of the cyclist.
Calculation:
Let's assume the direction of rain is towards the east and the speed of rain is v. The velocity of the cyclist is 10m/s towards the south and the velocity of the rain is 25m/s vertically downwards.
Using Pythagoras theorem, we can find the magnitude of the apparent speed of the rain as follows:
apparent speed = sqrt(v^2 + 10^2)
apparent speed = sqrt(v^2 + 100)
The direction of the apparent speed of rain can be found using trigonometry as follows:
tan(theta) = v/10
theta = tan^-1(v/10)
The direction of the apparent speed of rain is towards the east at an angle of theta from the south.
Conclusion:
The apparent speed of rain as seen by the cyclist is sqrt(v^2 + 100) m/s, where v is the speed of rain towards the east. The direction of the apparent speed of rain is towards the east at an angle of tan^-1(v/10) from the south.
When rain falls vertically, its speed is equal to the speed of gravity, which is 9.8m/s^2.
Apparent Speed:
The apparent speed of rain as seen by the cyclist is the vector sum of the speed of rain and the speed of the cyclist.
Direction of Rain:
The direction of rain as seen by the cyclist is the direction of the vector sum of the speed of rain and the speed of the cyclist.
Calculation:
Let's assume the direction of rain is towards the east and the speed of rain is v. The velocity of the cyclist is 10m/s towards the south and the velocity of the rain is 25m/s vertically downwards.
Using Pythagoras theorem, we can find the magnitude of the apparent speed of the rain as follows:
apparent speed = sqrt(v^2 + 10^2)
apparent speed = sqrt(v^2 + 100)
The direction of the apparent speed of rain can be found using trigonometry as follows:
tan(theta) = v/10
theta = tan^-1(v/10)
The direction of the apparent speed of rain is towards the east at an angle of theta from the south.
Conclusion:
The apparent speed of rain as seen by the cyclist is sqrt(v^2 + 100) m/s, where v is the speed of rain towards the east. The direction of the apparent speed of rain is towards the east at an angle of tan^-1(v/10) from the south.
Community Answer
Rain is falling vertically with a speed of 25m/s.A cyclist is going at...
Is it. 26.9 m/s ?
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Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain?
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Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain?.
Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rain is falling vertically with a speed of 25m/s.A cyclist is going at a speed of 10m/s in the north to south direction.what is apparent speed and direction of the rain?.
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