Question

A tower has an observation deck about 200 m above ground level. About how far is it from the observation deck horizen knowing that the earth's radius is 6400km?

Answer 1

He is a a distance of 50.597 km from the observable deck of horizon.

Explanation:

The distance from a height 'h' to the observable horizon ignoring the effects due to refraction in atmosphere is given by the formula

`d=√(h(2R+h))`

where

d = distance to observable horizon

h = height of observer from the sea level

R = Radius of earth

Applying the values we get

`d=√(0.2* (2* 6400+0.2))\\\\\therefore d=50.597km`

Answer 2

Answer: Horizon is 35777.64 m away from observation deck.

Explanation:

Since we have given that

Height of tower above ground level = 200 m

Radius of earth = 6400 km

Let R be the radius of earth.

Let the height of observation and

Let d be the distance from observation deck to horizon.

so, it makes a right angle triangle.

`(R+h)^2=R^2+d^2\\\\R^2+h^2+2Rh=R^2+d^2\\\\h^2+2Rh=d^2\\\\200^2+2* 6400000* 200=d^2\\\\40000+1280040000=d^2\\\\1280040000=d^2\\\\√(1280040000)=d\\\\d=35777.64\ km`

Hence, horizon is 35777.64 m away from observation deck.