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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 100 m, the correct angle (in degree) of banking of the road should be given by :
Correct answer is '21.801'. 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: 21.801
Most Upvoted Answer
A circular curve of a highway is designed for traffic moving at 72km/h...
Explanation:
Given:
- Speed of traffic, v = 72 km/h
- Radius of the curved path, r = 100 m
To ensure the safety of vehicles traveling on a curved path, the road is banked at an angle. This angle is determined by the speed of traffic and the radius of the curved path. The correct angle of banking can be found using the following formula:
tan(θ) = v^2 / (r × g)
Where:
- θ is the angle of banking
- v is the speed of traffic
- r is the radius of the curved path
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Converting Speed:
To use the formula, we need to convert the speed from km/h to m/s:
v = 72 km/h × (1000 m/1 km) × (1 h/3600 s) = 20 m/s
Calculating Angle:
Substituting the given values into the formula, we can calculate the angle of banking:
tan(θ) = (20 m/s)^2 / (100 m × 9.8 m/s^2)
Simplifying this equation gives:
tan(θ) = 400 / 980
Taking the inverse tangent (arctan) of both sides, we can find the angle:
θ = arctan(400 / 980)
Using a calculator, we find:
θ ≈ 21.801 degrees
Therefore, the correct angle of banking for the road is approximately 21.801 degrees.
Given:
- Speed of traffic, v = 72 km/h
- Radius of the curved path, r = 100 m
To ensure the safety of vehicles traveling on a curved path, the road is banked at an angle. This angle is determined by the speed of traffic and the radius of the curved path. The correct angle of banking can be found using the following formula:
tan(θ) = v^2 / (r × g)
Where:
- θ is the angle of banking
- v is the speed of traffic
- r is the radius of the curved path
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Converting Speed:
To use the formula, we need to convert the speed from km/h to m/s:
v = 72 km/h × (1000 m/1 km) × (1 h/3600 s) = 20 m/s
Calculating Angle:
Substituting the given values into the formula, we can calculate the angle of banking:
tan(θ) = (20 m/s)^2 / (100 m × 9.8 m/s^2)
Simplifying this equation gives:
tan(θ) = 400 / 980
Taking the inverse tangent (arctan) of both sides, we can find the angle:
θ = arctan(400 / 980)
Using a calculator, we find:
θ ≈ 21.801 degrees
Therefore, the correct angle of banking for the road is approximately 21.801 degrees.
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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 (in degree) of banking of the road should be given by :Correct answer is '21.801'. 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 (in degree) of banking of the road should be given by :Correct answer is '21.801'. 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 (in degree) of banking of the road should be given by :Correct answer is '21.801'. 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 (in degree) of banking of the road should be given by :Correct answer is '21.801'. Can you explain this answer?.
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