See this link.
Further hints on #2 and #3 will follow later this evening.
UPDATE: the equation for the parabola had an "R squared," but that should have been just "R." The error has been corrected in the linked file.
DOUBLE SECRET UPDATE: Problem 3 was assigned in MIT's course 8.01*, F03 semester. Check out their OpenCourseWare.
* MIT's courses are all numbered. Course 8 is physics, class 1 is mechanics. Course 18 is mathematics. Everything is numbered at MIT. Some of the buildings don't even have names. I worked in building 8 for a time, and later building NW-14.
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