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Earth is roughly 8000 miles in diameter.

 

(a) I'm riding in a hot air balloon 1 mile above the surface of earth. Approximately how far away is the horizon? (In other words, how far away is the farthest point on the surface of Earth that I can see.)

 

(b) What if I'm in a plane 6 miles above the surface of the earth?

 

(c) What is I'm in a spaceship 100 miles above the surface of the earth?

Mathgenius  Oct 6, 2018
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The radius of the Earth  = 8000/2  = 4000 miles

 

We  can  figure the distance  to the horizon  using a right triangle

 

The distance from  the center of the Earth to any object above the Earth's surface  = the hypotenuse = 4000  + h      where h is the height of the object [in  miles ] above the Earth's surface

 

And the radius of the Earth  is equal to one leg of the right triangle

 

And the distance from the object to the horizon, D,  is the other leg

 

So...we have this general formula to determine D

 

D  = √ [ (4000 + h)^2  - 4000^2]

 

So....

 

(a)  D  = √ [ (4000 + 1)^2  - 4000^2 ]  ≈ 89.4 miles

 

(b)  D  =   √ [ (4000 + 6)^2  - 4000^2 ]  ≈  219.2  miles

 

(c)  D  = √ [ (4000 + 100)^2  - 4000^2 ]  = 900 miles

 

 

cool cool cool

CPhill  Oct 6, 2018

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