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At the Earth's surface, a projectile is launched straight up at a speed of 9.9 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth.


  • Physics -

    (1/2) m v^2 = potential energy

    potential energy is mgh for low altitude but that will not work for high altitude where g is less than 9.81 m/s^2

    increase in potential = G M m (1/Re - 1/(Re+h)

    call z = Re +h

    (1/2) v^2 = G M (1/Re - 1/z)

    solve for z
    then h = z - Re

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