Question

Pam’s eye-level height is 324 ft above sea level, and Adam’s eye-level height is 400 ft above sea level. How much farther can Adam see to the horizon? Use the formula with d being the distance they can see in miles and h being their eye-level height in feet. 1 mi

Answer 1

The answer is √6 mi.

The formula is: d = √(3h/2)

Pam:
h = 324 ft
d = √(3 * 324/2) = √486 = √(81 * 6) = √81 * √6 = 9√6 mi

Adam:
h = 400 ft
d = √(3 * 400/2) = √600 = √(100 * 6) = √100 * √6 = 10√6 mi

How much farther can Adam see to the horizon?
Adam - Pam = 10√6 - 9√6 = √6 mi

Answer 2

The Adam can see the horizon at the distance of 2.45 miles

Given data:

Pam's eye-level height above the sea-level is, h = 324 ft.

Adam's eye-level height above sea level is, h' = 400 ft.

The distance of Pam from the horizon can be given as,

$d=\sqrt{3 \times \dfrac{h}{2} }$

Substitute the values as,

$d=\sqrt{3 \times \dfrac{324}{2} }\\d=22.04 \;\rm mi$

And, the distance of Adam from the horizon can be calculated as,

$d'=\sqrt{3 \times \dfrac{h'}{2} }\\\\d'=\sqrt{3 \times \dfrac{400}{2} }\\\\d'=24.49 \;\rm mi$

The net distance by Adam too see the horizon is,

$d_{net}=d'-d\\d_{net}=24.49 - 22.04\\d_{net}=2.45 \;\rm mi$

Thus, we can conclude that Adam can see the horizon at the distance of 2.45 miles.

Learn more about the horizon and its distance from here:

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