Answer:
4R/3
Explanation:
r = Distance from the surface of the Earth
R = Radius of Earth
G = Gravitational constant
M = Mass of Earth
m = Mass of satellite
v²= GM/2R
Loss of Kinetic energy is equal to Gain in potential energy
[tex]\frac{1}{2}mv^2=\frac{GMm}{R}-\frac{GMm}{r}\\\Rightarrow \frac{1}{2}m\frac{GM}{2R}=GMm\left(\frac{1}{R}-\frac{1}{r}\right)\\\Rightarrow \frac{1}{2}\frac{1}{2R}=\frac{r-R}{Rr}\\\Rightarrow \frac{1}{4}=\frac{r-R}{r}\\\Rightarrow r=4r-4R\\\Rightarrow -3r=-4R\\\Rightarrow r=\frac{4}{3}R[/tex]
∴ The farthest the projectile reaches from the center of the earth is [tex]\mathbf{\frac{4}{3}R}[/tex]
