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A circular curve of a highway is designed for traffic moving at 72 km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value of nAnswer
Correct answer is '0.4'. Can you explain this answer?
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A circular curve of a highway is designed for traffic moving at 72km/h...
The correct answer is: 0.4
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A circular curve of a highway is designed for traffic moving at 72km/h...
Introduction:
In this problem, we are given the speed and radius of a circular curve on a highway. We need to find the correct angle of banking for the road. The angle of banking is the angle at which the road is inclined towards the center of the curve. This angle helps to prevent vehicles from skidding sideways when taking the curve at high speeds.
Given:
Speed of traffic (v) = 72 km/h = 20 m/s
Radius of curved path (r) = 100 m
Formula:
The formula to calculate the correct angle of banking (θ) is given by:
tan(θ) = v^2 / (g * r)
where g is the acceleration due to gravity (9.8 m/s^2).
Solution:
Step 1: Convert the speed from km/h to m/s.
Speed (v) = 72 km/h = (72 * 1000) m / (60 * 60) s = 20 m/s
Step 2: Plug in the values into the formula.
tan(θ) = (20)^2 / (9.8 * 100)
Step 3: Calculate the value of tan(θ).
tan(θ) = 400 / 980 = 0.408
Step 4: Solve for θ.
θ = tan^(-1)(0.408)
Step 5: Use a calculator to find the value of θ.
θ ≈ 21.80 degrees
Step 6: Round the angle to one decimal place.
θ ≈ 21.8 degrees
Final Answer:
The correct angle of banking for the road is approximately 21.8 degrees, which can be rounded to 22 degrees. However, the given correct answer is 0.4, which does not match the calculated value. It seems there may be an error in the question or the provided answer.
In this problem, we are given the speed and radius of a circular curve on a highway. We need to find the correct angle of banking for the road. The angle of banking is the angle at which the road is inclined towards the center of the curve. This angle helps to prevent vehicles from skidding sideways when taking the curve at high speeds.
Given:
Speed of traffic (v) = 72 km/h = 20 m/s
Radius of curved path (r) = 100 m
Formula:
The formula to calculate the correct angle of banking (θ) is given by:
tan(θ) = v^2 / (g * r)
where g is the acceleration due to gravity (9.8 m/s^2).
Solution:
Step 1: Convert the speed from km/h to m/s.
Speed (v) = 72 km/h = (72 * 1000) m / (60 * 60) s = 20 m/s
Step 2: Plug in the values into the formula.
tan(θ) = (20)^2 / (9.8 * 100)
Step 3: Calculate the value of tan(θ).
tan(θ) = 400 / 980 = 0.408
Step 4: Solve for θ.
θ = tan^(-1)(0.408)
Step 5: Use a calculator to find the value of θ.
θ ≈ 21.80 degrees
Step 6: Round the angle to one decimal place.
θ ≈ 21.8 degrees
Final Answer:
The correct angle of banking for the road is approximately 21.8 degrees, which can be rounded to 22 degrees. However, the given correct answer is 0.4, which does not match the calculated value. It seems there may be an error in the question or the provided answer.
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A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer?
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A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer?.
A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer?.
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A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer?, a detailed solution for A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer? has been provided alongside types of A circular curve of a highway is designed for traffic moving at 72km/h. If the radius of the curved path is 100m, the correct angle of banking of the road should be given by :n tan-1(n). Find the value ofnAnswerCorrect answer is '0.4'. Can you explain this answer? theory, EduRev gives you an
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