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A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is?
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A lighthouse is visible just above the horizon at a certain station at...
Height of the Lighthouse Calculation
Given Information:
- Distance between the station and the lighthouse = 60 km
- Lighthouse is visible just above the horizon at the sea level
Understanding the Problem:
In this problem, we need to determine the height of the lighthouse. Since the lighthouse is visible just above the horizon, it means that the observer at the sea level station cannot see the entire height of the lighthouse. Therefore, we need to consider the curvature of the Earth while calculating the height of the lighthouse.
Curvature of the Earth:
The Earth is not completely flat, it has a curvature. The curvature decreases the line of sight of an observer, especially when the distance between the observer and the object increases. As the distance increases, the observer's line of sight tends to become tangential to the Earth's surface. This is why the lighthouse appears just above the horizon.
Calculating the Height:
To calculate the height of the lighthouse, we need to consider the curvature of the Earth. The formula to calculate the curvature is:
Curvature = (Distance^2) / (2 x Earth's Radius)
Substituting Values:
Given that the distance between the station and the lighthouse is 60 km. We can use this value to calculate the curvature.
Earth's radius is approximately 6371 km.
Substituting these values in the curvature formula:
Curvature = (60^2) / (2 x 6371) = 3600 / 12742 = 0.282 km
Calculating the Height:
To find the height of the lighthouse, we can use the following formula:
Height = Curvature + Observer's Eye Level
Substituting Values:
Since the observer is at the sea level, the observer's eye level is 0 km.
Substituting the values in the height formula:
Height = 0.282 + 0 = 0.282 km
Final Answer:
The height of the lighthouse is approximately 0.282 km, considering the curvature of the Earth.
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A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is?
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A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is?.
A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lighthouse is visible just above the horizon at a certain station at the sea level. Distance between the station and the lighthouse is 60 km. The height of the lighthouse is?.
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