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vlada-n [284]
3 years ago
8

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
Physics
1 answer:
Scilla [17]3 years ago
6 0

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}

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