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Which one of the following gives the correct distance between the lighthouse and a ship, when the lighthouse whose height is 100 m is visible just above the horizon from the ship?
- a)30.68 km
- b)36.50 km
- c)38.54 km
- d)40.54 km
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which one of the following gives the correct distance between the ligh...
If d is the distance to the visible horizon, it is given by,
‘C' being in metres,
∴
‘C' being in metres,
∴
Most Upvoted Answer
Which one of the following gives the correct distance between the ligh...
Given data:
Height of the lighthouse, H = 100 m
Let the distance between the ship and the lighthouse be 'd'.
Let the radius of the Earth be 'R'.
To find: the distance between the ship and the lighthouse (d)
Calculation:
From the given data, we can form a right-angled triangle with the lighthouse at the top, the observer at the bottom, and the line of sight as the hypotenuse.
Let 'r' be the distance of observer's eye level above the sea level.
Using the Pythagorean theorem, we have:
d² = (R + r)² - R²
Also, we know that:
r/H = tan(0.53°)
r = H × tan(0.53°)
Substituting the value of 'r' in the above equation, we get:
d² = (R + H × tan(0.53°))² - R²
On substituting the given values, we get:
d² = (6370 + 100 × tan(0.53°))² - 6370²
d = √((6370 + 100 × tan(0.53°))² - 6370²)
d ≈ 38.54 km
Therefore, the correct answer is option (c) 38.54 km.
Height of the lighthouse, H = 100 m
Let the distance between the ship and the lighthouse be 'd'.
Let the radius of the Earth be 'R'.
To find: the distance between the ship and the lighthouse (d)
Calculation:
From the given data, we can form a right-angled triangle with the lighthouse at the top, the observer at the bottom, and the line of sight as the hypotenuse.
Let 'r' be the distance of observer's eye level above the sea level.
Using the Pythagorean theorem, we have:
d² = (R + r)² - R²
Also, we know that:
r/H = tan(0.53°)
r = H × tan(0.53°)
Substituting the value of 'r' in the above equation, we get:
d² = (R + H × tan(0.53°))² - R²
On substituting the given values, we get:
d² = (6370 + 100 × tan(0.53°))² - 6370²
d = √((6370 + 100 × tan(0.53°))² - 6370²)
d ≈ 38.54 km
Therefore, the correct answer is option (c) 38.54 km.
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Which one of the following gives the correct distance between the lighthouse and a ship, when the lighthouse whose height is 100 m is visible just above the horizon from the ship?a)30.68 kmb)36.50 kmc)38.54 kmd)40.54 kmCorrect answer is option 'C'. Can you explain this answer?
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