anonymous
  • anonymous
Two sailors are at the top of their ships' masts in the open ocean. The mast of ship A is twice as high as that of ship B. How much farther can sailor A see than sailor B?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
a) no farther b) a little more than 40% farther c) twice as far d) almost three times as far e) four times as far
anonymous
  • anonymous
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anonymous
  • anonymous
R is the radius of the Earth, r is the line of sight up to the curvature of the Earth, h is the height of the ship and mast.

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anonymous
  • anonymous
It seems to me, unless I'm doing it wrong, that, to find r (the line of sight), I need to have h (the height of the mast), but to find h, I need r. I can't find one without having the other.
anonymous
  • anonymous
Or am I just going about this the wrong way?
anonymous
  • anonymous
I am given the radius of the Earth as 6.37 * 10^6 m, but I am not given a height.
anonymous
  • anonymous
But it isn't really asking for the height, it just wants to know how much farther the ship with the twice-as-tall mast can see.
anonymous
  • anonymous
\[d_1^2=(R_E+h_1)^2-R_E^2=2R_Eh_1+h_1^2=h_1(2R_E+h_1)\]\[d_2^2=(R_E+h_2)^2-R_E^2=2R_Eh_2+h_2^2=h_2(2R_E+h_2)\]We may assume that \[h_1<

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