Posted by **Alice** on Friday, December 27, 2013 at 4:34pm.

We release an object of mass M at zero speed at a distance of 2*10^6 Km from the center of the earth. What is the speed at which the object hits the earth?

G=6.67*10^-11; g= 9.8 m/s; M=5.97*10^24;

r=6.3781*10^6

Suppose the mass of the object is M= 500 kg. What is the kinetic energy of this object when it hits the earth?

Thanks for your help.

- physics -
**Elena**, Friday, December 27, 2013 at 6:29pm
M= 5.97•10²⁴ kg

m=500 kg

r = 6.378•10⁶ m.

R= 2• 0⁶ km= 2• 10⁹ m

GmM/r-GmM/R = mv²/2

GM(1/r -1/R) = v²/2

v=sqrt{2GM(r-R)/rR}=

=sqrt {2•6.67•10⁻¹¹• 5.97•10²⁴(2• 10⁹ - 6.3781•10⁶)/2• 10⁹•6.3781•10⁶}=

=1.1•10⁴ m/s

mv²/2 = 500•(1.1•10⁴)²/23.025 •10¹º J

- physics -
**Alice**, Saturday, December 28, 2013 at 9:15am
Thanks Elena for your help. I have been having trouble with some of these equations.

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