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A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella?
Verified Answer
A person is standing on a road by holding his umberella at right angle...
Velocity of Rain(Vr) = 10 m/sec
Velocity of Wind(Vw) = 20m/sec
The person have to turn his umbrella in the resultant of the velocity of rain and wind in order to protect himself from the rain.
Then Angle = Velocity of Rain(Vr) / Velocity of Wind(Vw)
= 1/2
= tan-1(1/2)
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Most Upvoted Answer
A person is standing on a road by holding his umberella at right angle...
Can u explain it well the answer is tan^-1(2) wrt the initial position umbrella towards 30 degrees north of east
Community Answer
A person is standing on a road by holding his umberella at right angle...
Analysis:
To determine the angle at which the person needs to turn his umbrella, we need to consider the rain's velocity and the wind's velocity. Let's break down the problem step by step:
Step 1: Analyzing the Rain's Velocity:
- The rain is falling at a speed of 10 m/s.
- Since the person is holding the umbrella at a right angle to the horizontal surface, the umbrella's surface should be perpendicular to the rain's direction of motion.
Step 2: Analyzing the Wind's Velocity:
- The wind is blowing at a speed of 20 m/s towards 30 degrees south of west.
- We can break down the wind's velocity into two components: one along the west direction and one along the south direction.
Step 3: Finding the Components of Wind's Velocity:
- The component of wind's velocity along the west direction is given by: 20 m/s * cos(30°).
- The component of wind's velocity along the south direction is given by: 20 m/s * sin(30°).
Step 4: Combining Rain and Wind Velocities:
- To determine the effective velocity of rain hitting the person, we need to combine the rain's velocity and the wind's velocity.
- We can add the west component of wind's velocity to the rain's velocity because they are both in the same direction.
- We can subtract the south component of wind's velocity from the rain's velocity because they are in opposite directions.
Step 5: Calculating the New Angle:
- The new angle at which the person needs to turn his umbrella is the angle between the effective velocity of rain and the horizontal surface.
Step 6: Applying Trigonometry:
- We can use trigonometry to find the new angle.
- Let's assume the angle between the effective velocity of rain and the horizontal surface is θ.
- We know the magnitude of the effective velocity of rain (10 m/s) and the components of wind's velocity along the west and south directions.
- We can use the tangent function to find θ: tan(θ) = (west component of wind's velocity - rain's velocity) / (rain's velocity + south component of wind's velocity).
Step 7: Calculating the New Angle:
- We can solve the equation obtained in Step 6 to find the value of θ.
Step 8: Final Answer:
- The person needs to turn his umbrella by the angle obtained in Step 7 in order to protect himself from the rain.
To determine the angle at which the person needs to turn his umbrella, we need to consider the rain's velocity and the wind's velocity. Let's break down the problem step by step:
Step 1: Analyzing the Rain's Velocity:
- The rain is falling at a speed of 10 m/s.
- Since the person is holding the umbrella at a right angle to the horizontal surface, the umbrella's surface should be perpendicular to the rain's direction of motion.
Step 2: Analyzing the Wind's Velocity:
- The wind is blowing at a speed of 20 m/s towards 30 degrees south of west.
- We can break down the wind's velocity into two components: one along the west direction and one along the south direction.
Step 3: Finding the Components of Wind's Velocity:
- The component of wind's velocity along the west direction is given by: 20 m/s * cos(30°).
- The component of wind's velocity along the south direction is given by: 20 m/s * sin(30°).
Step 4: Combining Rain and Wind Velocities:
- To determine the effective velocity of rain hitting the person, we need to combine the rain's velocity and the wind's velocity.
- We can add the west component of wind's velocity to the rain's velocity because they are both in the same direction.
- We can subtract the south component of wind's velocity from the rain's velocity because they are in opposite directions.
Step 5: Calculating the New Angle:
- The new angle at which the person needs to turn his umbrella is the angle between the effective velocity of rain and the horizontal surface.
Step 6: Applying Trigonometry:
- We can use trigonometry to find the new angle.
- Let's assume the angle between the effective velocity of rain and the horizontal surface is θ.
- We know the magnitude of the effective velocity of rain (10 m/s) and the components of wind's velocity along the west and south directions.
- We can use the tangent function to find θ: tan(θ) = (west component of wind's velocity - rain's velocity) / (rain's velocity + south component of wind's velocity).
Step 7: Calculating the New Angle:
- We can solve the equation obtained in Step 6 to find the value of θ.
Step 8: Final Answer:
- The person needs to turn his umbrella by the angle obtained in Step 7 in order to protect himself from the rain.
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A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella?
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A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella?.
A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person is standing on a road by holding his umberella at right angle to the horizontal surface in order to protect himself from rain falling at a speed of 10ms and where as velocity of wind is 0. suddenly wind begins to blow at speed of 20 ms towards 30 degrees south of west now by ehat angle he has to turn his umberella?.
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