How high do we need to be on Earth to see 7 miles? On Earth, the distance to the horizon is given by $d \approx \sqrt { \frac { 3 h } { 2 } }$ , where d is in miles to the horizon and h is in feet above sea level.
A) $32 \frac { 2 } { 3 }$ feet
B) $31 \frac { 2 } { 3 }$ feet
C) $34 \frac { 1 } { 4 }$ feet
D) $2 \frac { 2 } { 3 }$ feet
E) $10 \frac { 2 } { 3 }$ feet

Question

Quizplus · Accepted Answer

To see 7 miles, we set $d = 7$ and solve for $h$ in the equation $d = \sqrt{\frac{3h}{2}}$. Rearranging and solving for $h$, we get $h = \frac{2d^2}{3}$. Substituting $d = 7$, we find $h = \frac{2(7)^2}{3} = \frac{98}{3} = 32 \frac{2}{3}$ feet.

How High Do We Need to Be on Earth to See