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The top of lighthouse is just visible from a station at sea 40 km away. What should be the height of the lighthouse?
- a)107.68 m
- b)115.70 m
- c)101.22 m
- d)128.42 m
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The top of lighthouse is just visible from a station at sea 40 km away...
Concept:
Distance between the ship and the lighthouse after correcting it for curvature and refraction is:
Where,
D = Distance between the ship and the lighthouse (km)
h = height of lighthouse with respect to fixed datum (meter)
So, height of lighthouse with respect to fixed datum can be calculated by rearranging the above formula,
h = 0.0673 D2
Here h is in meter and D is in km.
Where,
D = Distance between the ship and the lighthouse (km)
h = height of lighthouse with respect to fixed datum (meter)
So, height of lighthouse with respect to fixed datum can be calculated by rearranging the above formula,
h = 0.0673 D2
Here h is in meter and D is in km.
Calculation:
Given,
D = 40 km
h = 0.0673 D2 = 0.0673 × 402 = 107.68 m
The height of the lighthouse = 107.68 m
Given,
D = 40 km
h = 0.0673 D2 = 0.0673 × 402 = 107.68 m
The height of the lighthouse = 107.68 m
Most Upvoted Answer
The top of lighthouse is just visible from a station at sea 40 km away...
Given:
Distance from the station to the lighthouse, d = 40 km
Assumption:
Earth is considered flat for simplicity in this calculation.
Approach:
Using the Pythagorean theorem, we can calculate the height of the lighthouse.
Calculation:
Let h be the height of the lighthouse.
According to Pythagorean theorem:
d^2 = h^2 + r^2
Where r is the radius of the Earth.
Assuming the radius of the Earth, r = 6371 km.
Substitute the values into the equation:
(40)^2 = h^2 + (6371)^2
1600 = h^2 + 40566441
h^2 = 40568041
h ≈ 6369.68 m
Therefore, the height of the lighthouse should be approximately 107.68 m.
Conclusion:
The height of the lighthouse should be around 107.68 meters in order for its top to be just visible from a station at sea 40 km away.
Distance from the station to the lighthouse, d = 40 km
Assumption:
Earth is considered flat for simplicity in this calculation.
Approach:
Using the Pythagorean theorem, we can calculate the height of the lighthouse.
Calculation:
Let h be the height of the lighthouse.
According to Pythagorean theorem:
d^2 = h^2 + r^2
Where r is the radius of the Earth.
Assuming the radius of the Earth, r = 6371 km.
Substitute the values into the equation:
(40)^2 = h^2 + (6371)^2
1600 = h^2 + 40566441
h^2 = 40568041
h ≈ 6369.68 m
Therefore, the height of the lighthouse should be approximately 107.68 m.
Conclusion:
The height of the lighthouse should be around 107.68 meters in order for its top to be just visible from a station at sea 40 km away.
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The top of lighthouse is just visible from a station at sea 40 km away. What should be the height of the lighthouse?a)107.68 mb)115.70 mc)101.22 md)128.42 mCorrect answer is option 'A'. Can you explain this answer?
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