The kinetic energy the person would need is [tex]4.5\cdot 10^9 J[/tex]
Explanation:
The formula to calculate the escape velocity from the surface of a planet is:
[tex]v=\sqrt{\frac{2GM}{R}}[/tex]
where
G is the gravitational constant
M is the mass of the planet
R is its radius
For the Earth, we have
[tex]M=5.97\cdot 10^{24} kg[/tex]
[tex]R=6.37\cdot 10^6 m[/tex]
Substituting, we find the escape velocity from the Earth:
[tex]v=\sqrt{\frac{2(6.67\cdot 10^{-11})(5.97\cdot 10^{24})}{6.37\cdot 10^6}}=1.18\cdot 10^4 m/s[/tex]
The kinetic energy that a person of 65 kg would need to escape from the Earth's gravitational field is therefore
[tex]K=\frac{1}{2}mv^2[/tex]
where
m = 65 kg is the mass of the man
[tex]v=1.18\cdot 10^4 m/s[/tex] is the escape velocity
And substituting, we find:
[tex]K=\frac{1}{2}(65)(1.18\cdot 10^4)^2=4.5\cdot 10^9 J[/tex]
Learn more about kinetic energy:
brainly.com/question/6536722
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