Asked by Ayana
How far would a submarine periscope have to be above the water for lookout to locate a ship 5 miles away?
Answers
Answered by
Anonymous
I assume you have a formula for the distance to the horizon for a given height ...
Answered by
mathhelper
I don't know what formula you have been given, but a more or less
general one states
d = √(2h R), where R is the radius , h is the height above the water, and
d is the distance we can see, as long we use the same units throughout.
The radius of the earth is appr 4000 miles
so we want
3 = √(8000h)
9 = 8000h
h = 9/8000 miles
but we probably want this in feet, so multiply by 5280
height = 9/8000*5280 = appr 5.94 ft
general one states
d = √(2h R), where R is the radius , h is the height above the water, and
d is the distance we can see, as long we use the same units throughout.
The radius of the earth is appr 4000 miles
so we want
3 = √(8000h)
9 = 8000h
h = 9/8000 miles
but we probably want this in feet, so multiply by 5280
height = 9/8000*5280 = appr 5.94 ft
Answered by
mathhelper
oops,
should have been 5 miles instead of 3
I will let you make the necessary changes.
Let me know what your answer is.
should have been 5 miles instead of 3
I will let you make the necessary changes.
Let me know what your answer is.
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