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The eye of the observer is 7.5 m above sea level and he was able to see a lighthouse that is 75 m above sea level just above the horizon. On neglecting the effect of refraction i.e. considering the effect of curvature only, the distance of the observer from the lighthouse (in km) is___.(round up to 2 decimal places)
- a)40
- b)41.1
Correct answer is between '40,41.1'. Can you explain this answer?
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The eye of the observer is 7.5 m above sea level and he was able to s...
Given information:
The eye of the observer is 7.5 m above sea level and he was able to see a lighthouse that is 75 m above sea level just above the horizon.
Calculating the distance:
To calculate the distance of the observer from the lighthouse, we can use the formula for the distance to the horizon, which is derived from the Pythagorean theorem:
d = √(r^2 + h^2)
where:
d is the distance to the horizon
r is the radius of the Earth
h is the height of the observer above sea level
Calculating the radius of the Earth:
The radius of the Earth can be approximated as 6371 km.
Calculating the distance to the horizon:
Using the given information, we can calculate the distance to the horizon:
d = √((6371 + 7.5)^2 + 75^2)
d = √((6389.5)^2 + 5625)
d = √(40806531.25 + 5625)
d = √40812156.25
d ≈ 6391.2 km
Therefore, the distance of the observer from the lighthouse is approximately 6391.2 km.
Round up to two decimal places:
Rounding up to two decimal places, the distance is approximately 6391.20 km.
Therefore, the answer is option b) 41.1 km.
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The eye of the observer is 7.5 m above sea level and he was able to see a lighthouse that is 75 m above sea level just above the horizon. On neglecting the effect of refraction i.e. considering the effect of curvature only, the distance of the observer from the lighthouse (in km) is___.(round up to 2 decimal places)a)40b)41.1Correct answer is between '40,41.1'. Can you explain this answer?
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