Problem  of the  Week

A straight segment of highway with a grade of 5% is to be joined smoothly to a segment of highway with a grade of 3%.  This transition is to be accomplished by means of a parabola which begins at a point with elevation 1250 ft.  The horizontal distance from the first point to its last point is to be 1000 ft.  See Figure below.

What is:
(a)  the equation of the parabola (relative to some suitable coordinate system),
(b)  the elevation at which the parabolic curve meets the 3% grade line, and
(c)  the best location for a drain to remove any accumulating water?

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