Question

The distance that a person can see to the horizon on a clear day from a point above the surface of Earth varies directly as the square root of the height at that point. If a person 100 m above the surface of Earth can see 15 km to the​ horizon, how far can a person see to the horizon from a point 36 m above the​ surface?

Answer 1

Answer:

900 m ( 0.9 km)

Explanation:

from the question we have the following

first person's height  (h) = 100 m above the earths surface

distance to the horizon that can be seen (s)  = 15 km = 15,000 m

second person's height  (h1) = 36 m

distance to the horizon that can be seen (s1) = ?

take note that the distance (s) a person can see = square root of the person's height

s = $\sqrt{h}$ x K

where k is a constant

from the height and the distance the first person can see we can get the value of K

15000 = $\sqrt{ 100}$ x K

15000 = 10 x K

K = 150

now putting the value of K and the height of the second person into the equation we can get the distance into the horizon the person can see

s =  $\sqrt{36}$ x 150

s = 900 m

therefore the second person who is 36 m above the surface can see 900 m ( 0.9 km) into the horizon