Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula $D = \sqrt { 2 r h + h ^ { 2 } }$ where r = 3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tower, 1000 ft above the ground? Round the answer to one decimal place
A)37.9 mi
B)428.1 mi
C)1428.4 mi
D)73.9 mi
E)none of these

Question

Quizplus · Accepted Answer

First, convert the height from feet to miles: $1000 \text{ ft} = \frac{1000}{5280} \text{ miles}$ since there are 5280 feet in a mile. Then, plug the values into the formula: $D = \sqrt{2 \times 3960 \times \frac{1000}{5280} + \left(\frac{1000}{5280}\right)^2}$. Simplifying this gives a value that does not match any of the provided options exactly, hence the correct choice is E, "none of these."

Due to the Curvature of the Earth, the Maximum Distance D=2rh+h2D = \sqrt { 2 r h + h ^ { 2 } }D=2rh+h2​

Due to the Curvature of the Earth, the Maximum Distance $D = \sqrt { 2 r h + h ^ { 2 } }$