Question

A sailor at the seashore watches a ship with a smokestack 30 meters above water level as the ship steams out to sea. The sailor's eye level is 4 meters above water level. About how far is the ship from shore when the stack disappears from the sailor's view? (The radius of Earth is about 6400 kilometers.)

Answer 1

how far is the ship from shore when the stack disappears from the sailor's view =29.73 m

Explanation:

you will see this makes a right triangle

the height is 6,400,000 m+4 m=6,400,004m

the hypotenuse is 6,400,000 m+30 m=6,400,030m

By Pythagorus theorem:

the distance of the ship D^2= 6,400,030^2- 6,400,004^2

= (6,400,030- 6,400,004)x( 6,400,030+ 6,400,004)

[because a^2-b^2=(a-b)x(a+b)]

=26x34

D^2=884 m

D= 29.73 m