Question

Assume nothing else blocks their view, approximately how far can two people stand from each other in clear atmosphere until they can no longer see each other due to the curvature of the Earth? [Take radius of earth $=6400km$]
(Assume height of each person is $2m$.)

• A. 10 m
• B. 100 m
• C. 1 km
• D. 10 km

Answer 1

The correct option is C 1 km

Given:

Height of each person $h=2m$

Radius of earth, $R=6400km=6400000m$

For a right angled triangle, we see the hypotenuse is $R+2.$

Base and perpendicular are $R$ and $X$ respectively.

Using Pythagoras theorem,

$(R+2{)}^2=R^2+X^2$

$X=\sqrt{(R+2{)}^2-R^2}$

The distance we need to find is the length of the tangent $2X$.

So,

$\begin{array}{c}2X=2\sqrt{{\left(R+2\right)}^2-R^2}\\ =2\sqrt{2\left(2R+2\right)}\\ =4\sqrt{R+1}\\ =4\sqrt{6400001M}\\ =10119.3m\approx 1km\\ Ans.\left(C\right)\end{array}$

If both the people move farther than this distance, their vision will be blocked by the curvature of the earth.