What would be the projections velocity of a satellite so that intersteller (interspace with no gravitation) velocity of the satellite becomes the orbital velocity when it is in the orbit at height of `10R` from earth's surface, where `R` is the radius of the earth?

Options

A. `(Tsqrt(2))/8`
B. `(Tsqrt(2))/16`
C. `(Tsqrt(2))/4`
D. `(Tsqrt(2))/32`

Answer

A

Explanation

Intersteller velocity `v'=sqrt((GM)/r)=Rsqrt(g/((R+h)))`
`=sqrt(v^(2)-v_(e)^(2))`
Where `v`=projection velocity
`(R^(2)g)/((r+h))=v^(2)-2gR` solving `v^(2)=(23gR)/11`