Respuesta :
Answer:
The minimum total speed is 11.2km/s
Explanation:
We are been asked to find the escape velocity.
Escape velocity is defined as the minimum initial velocity that will take a body(projectile)away above the surface of a planet(earth) when it's projected vertically upwards.
The formula to calculate the escape velocity is Ve = √2gR
For the earth g = 9.8m/s2 , R = 6.4*10^6
Substituting into the equation Ve = √2*9.8*6.4*10^6 = 11.2*10^3m/s
=11.2km/s
Answer:
escape velocity comes out to be = [tex]11kms^{-1}[/tex]
Explanation:
The escape velocity corresponds to the initial kinetic energy
Initial kinetic energy = [tex]\frac{1}{2} mv^{2}[/tex]
Also we know that work done in lifting the body from earth surface to an infinite distance is equal to the increase in its potential energy
Increase in P.E = 0 - [tex](-G\frac{Mm}{R} )=G\frac{Mm}{R}[/tex]
M= mass of earth
R=radius of earth
now
[tex]\frac{1}{2} mv^{2}[/tex] = G\frac{Mm}{R}[/tex]
[tex]V_{escape}[/tex] = [tex]\sqrt{\frac{2GM}{R} }[/tex]
As g = [tex]\frac{GM}{R^{2} }[/tex]
[tex]V_{escape}[/tex] = [tex]\sqrt{2gR}[/tex]
escape velocity can be calculated as by putting value of
g = [tex]9.8ms^{-2}[/tex]
R = radius of earth = 6400 km
escape velocity comes out to be = [tex]11kms^{-1}[/tex]