Question

A projectile is fired straight upward from earths surface with a speed c given by: v^2= GM/2R. Where M is the mass and R is the radius. The farthest the projectile reaches from the center of the earth is: 2R
5R/4
Infinity
4R
4R/3

Answer 1

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

$\frac{1}{2}mv^2=\frac{GMm}{R}-\frac{GMm}{r}\\\Rightarrow \frac{1}{2}m\frac{GM}{2R}=GMm\left(\frac{1}{R}-\frac{1}{r}\right)\\\Rightarrow \frac{1}{2}\frac{1}{2R}=\frac{r-R}{Rr}\\\Rightarrow \frac{1}{4}=\frac{r-R}{r}\\\Rightarrow r=4r-4R\\\Rightarrow -3r=-4R\\\Rightarrow r=\frac{4}{3}R$

∴ The farthest the projectile reaches from the center of the earth is $\mathbf{\frac{4}{3}R}$