Answer
11181 meters per second
Work Step by Step
Given:
$v=\sqrt{\dfrac{2Gm}{r}}$
$G=6.67\times10^{-11}m^3/kg\bullet s^2$.
mass of Earth is $5.97\times10^{24}$ kg
radius of Earth is $6.37\times10^6$ m
Find escape velocity for Earth in meters per second.
Plug in given information into the formula and solve:
$v=\sqrt{\dfrac{2(6.67\times10^{-11}m^3/kg\bullet s^2)(5.97\times10^{24}kg)}{6.37\times10^6m}}$
$v=\sqrt{\dfrac{7.96398\times10^{14}m^3/s^2}{6.37\times10^6m}}$
$v=\sqrt{125023233.9m^2/s^2}$
$v=11181.37889$ m/s
Round answer to the nearest whole number:
The escape velocity for Earth is 11181 meters per second.
