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

Please give me full explanation how to answer this question.

I want to know it for necessary.

Thank you so much.

Answer 1

$d=\sqrt{(R+h)^2-R^2}=\sqrt{2Rh+h^2},$

$h<<R,$

$d=\sqrt{2Rh},$

$\frac{d_2}{d_2}=\sqrt{\frac{h_2}{h_1}}=\sqrt{\frac{2h_1}{h_1}}=\sqrt 2.$

NO a) no farther

YES b) a little more than 40% farther

NO c) twice as far

NO d) almost three times as far

NO e) four times as far