Question

karylbs eye - level height is 48 ft above sea level, and addisons eye - level height is $85\frac{1}{3}$ ft above sea level. how much farther can addison see to the horizon? use the formula $d = \sqrt{\frac{3h}{2}}$, with $d$ being the distance they can see in miles and $h$ being their eye - level height in feet.
\\(\circ\\) \\(\sqrt{2}\\) mi
\\(\circ\\) \\(2\sqrt{2}\\) mi
\\(\circ\\) \\(14\sqrt{2}\\) mi
\\(\circ\\) \\(28\sqrt{2}\\) mi

Explanation:

Step1: Calculate Addison's distance

Given \( h_{Addison} = 85\frac{1}{3}=\frac{256}{3}\) ft, use \( d = \sqrt{\frac{3h}{2}} \).
Substitute \( h=\frac{256}{3} \):
\( d_{Addison}=\sqrt{\frac{3\times\frac{256}{3}}{2}}=\sqrt{\frac{256}{2}}=\sqrt{128}=8\sqrt{2} \) miles.

Step2: Calculate Karylib's distance

Given \( h_{Karylib} = 48 \) ft, use \( d = \sqrt{\frac{3h}{2}} \).
Substitute \( h = 48 \):
\( d_{Karylib}=\sqrt{\frac{3\times48}{2}}=\sqrt{72}=6\sqrt{2} \) miles.

Step3: Find the difference

Subtract \( d_{Karylib} \) from \( d_{Addison} \):
\( 8\sqrt{2}-6\sqrt{2}=2\sqrt{2} \) miles.

Answer:

\( 2\sqrt{2} \) mi (corresponding to the option " \( 2\sqrt{2} \) mi ")