I point this out due to question 13 on this year's New York State Regents Exam in Algebra II (Common Core) from June 1, 2016.:
Mathematically speaking, this question should be very simple. It is really just asking for the smallest value for H(t), and for an exam incorporating graphic calculators it is a snap.
Here is a GeoGebra model for one "car" on this wheel:
A more meaty question for Algebra II students would have been to identify the arc length between the position at time 0 and the bottom point on the trip.
Moral of the story: New York State, please stop hiding mathematics behind a veil of weakly designed "applications".