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    Gravitational Potential Energy: Changing Kinetic Energy

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    A projectile is given a vertical upward velocity Vo = 10000 m/sec at Earth's surface. Neglect air friction. Find the maximum distance it will achieve above the surface of Earth. Do not consider g to be constant.

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    Physics notes:
    Note: The starting point for this problem could be either of two choices.

    Note 1.
    Start with the expression giving the gravitational PE of two bodies of mass M and m, separated by center to center distance r, which is expressed by:
    (1) P.E. = - G M m/r
    Note that this quantity is negative because the P.E. is defined to be zero when the separation r is infinite. Therefore if r increases from some initial value, then for the P.E. to approach zero, it has to initially be a negative value.
    Note 2.
    By conservation of energy, as the projectile ...