A projectil is projected vertically upwards from Earth at what height above the earth's surface will the force on the satellite due to the Earth be reduced to half its value at the Earth station?

(1/2)Gm/R2=Gm/(R+h)2

Where:
G is the gravitational constant
m is the mass of the Earth
R is the Radius of the Earth
h is the height above the Earth where Gravity is 1/2 surface gravity

Canceling Gm from both sides gives:
1/2R2 = 1/(R+h)2

inverting to make things simpler:
2R2 = (R+h)2

taking the square root of both sides:
sqrt(2)R=R+h

(sqrt(2)-1)R=h

the sqrt(2)=1.4142135623730950488016887242097
(sqrt(2)-1) = 0.4142135623730950488016887242097

so h=0.4142 R

The required height is 0.41 times the radius of Earth.