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physics

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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 - ,

    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 - ,

    Thanks Elena for your help. I have been having trouble with some of these equations.

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