Question

what is escape velocity?

Answer 1

the initial velocity needed to escape the gravitational pull of Earth

Answer 2

$\textbf{Answer :}$



$\huge\textbf{Escape Velocity :}$


It is the minimum velocity required by an object to escape from gravitational field of a planet such that it never comes back.


$\textbf{Derivation :}$

Gravitational potential energy + kinetic energy = 0

$\frac{-GMm}{R}$ + $\frac{m v_{e} ^{2} }{2}$  = $0$

$\frac{m v_{e} ^{2} }{2}$ = $\frac{GMm}{R}$

$v_{e} ^{2}$  = $\frac{2GM}{R}$ 

$v_{e}$  =  $\sqrt{ \frac{2GM}{R} }$

$v_{e}$ = $11.2 km/s$

Also we know that

$g$ = $\frac{GM}{ R^{2} }$

$R^{2}$ = $GM$

$v_{e}$  = $\sqrt{ \frac{2 R^{2}g }{R} }$

$v_{e}$ = $\sqrt{2gR}$

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