A railroad one mile long is anchored at both ends. On a hot day it expands one foot and buckles. Approximately how high off the ground is it at its midpoint?

[Editor's Notes: (1) You can assume the buckled rail has the shape of an arc of a circle. Books on Strength of Materials would assume a parabolic shape. (2) The problem asks for an "approximate" answer; how "approximate" is your answer? Try to get upper and lower bounds for the true height.]

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