Posted by Alice on .
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,
M= 5.97•10²⁴ kg
m=500 kg
r = 6.378•10⁶ m.
R= 2• 0⁶ km= 2• 10⁹ m
GmM/rGmM/R = mv²/2
GM(1/r 1/R) = v²/2
v=sqrt{2GM(rR)/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,
Thanks Elena for your help. I have been having trouble with some of these equations.