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A rocket is fired straight up through the atmosphere from the South Pole, burning out at an altitude of 208 km when traveling at 5.8 km/s.
(a) What maximum distance from Earth's surface does it travel before falling back to Earth?

  • physics -

    The Earth's radius is Re = 6378 km.
    Burnout occurs when R = 6586 km.

    At the highest altitude, the burnout kinetic energy equals the gain in potential energy.
    (1/2) M V^2 = GM[1/R - 1/(R+h)]

    Solve for R+h. R+h-Re is the distance from the surface of the earth.

    M is the Earth's mass and G is the universal constant of gravity.

    In case you don't want to look up M and G,you can use the fact that

    GM/Re^2 = g = 9.81 m/s^2

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