Okay, here we have this;
Considering the provided equation, we are going to calculate how much farther a sailor can see when he is in the crows nest, so we obtain the following expression:
How much farther a sailor can see when he is in the crows nest=Distance to the horizon when at the crow's nest - Distance to the horizon when viewing from the deck
Replacing:
[tex]\begin{gathered} Difference=1.225\sqrt[]{100}-1.225\sqrt[]{40} \\ =12.25-\sqrt{10}\cdot\: 2.45 \\ \approx4.50 \end{gathered}[/tex]
Finally we obtain that from the crow's nest of the ship the sailor see approximately 4.50 miles farther than from the deck.
