Chapter A.2, Problem 53AYU

To determine

To find: How far can you see from the conning tower?

Answer to Problem 53AYU

$5.477$ miles

Explanation of Solution

Given:

The conning tower of the U.S.S. Silversides, a World War II submarine now permanently stationed in Muskegon, Michigan, is approximately 20 feet above sea level. How far can you see from the conning tower? [use the facts that the radius of Earth is 3960 miles and 1 mile $=5280$ feet].

Calculation:

$1\text{ miles }=5280\text{ feet}$.

$1\text{ foot }= \frac{1}{5280}\text{ miles}$.

$20\text{ feet }= \frac{20}{5280}\text{ miles = }\frac{1}{264} \text{miles}$.

By Pythagorean Theorem $c^2=a^2+b^2$.

${\left(3960+\frac{1}{264}\right)}^2=a^2+{3960}^2$

$15681630=a^2+15681600$

$a^2=30$

$a=5.477$

$5.477$ miles far can you see from the conning tower.