Answer to Question #241881 in Physics for OMAR

Question

Two sailors are at the tops 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?
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

Answer 1

For the first ship, we have

$$D_1=3.85\sqrt{h},\\ D_2=3.85\sqrt{2h}=1.41D_1.$$

Therefore, the higher mast increases the visibility distance by a bit more than 40%.