Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface.

Correct result:

h =  4252 km

Solution:

R=6378 km S1=4π R2=4 3.1416 63782511185932.5225 km2 S=1/5 S1=1/5 511185932.5225102237186.5045 km2 S=2πRv v=S/(2π R)=102237186.5045/(2 3.1416 6378)=127565=2551.2 y=Rv=63782551.2=191345=3826.8 x=R2y2=637823826.82=255125=5102.4 k=\cotanα=x/y=(h+v)/x x/y=(h+v)/x h+v=x2/y h=x2/yv=5102.42/3826.82551.2=4252 km



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