Ski Racing Parabolas

As an athlete, the concept of parabolas in sports caught my eye.  There are the obvious ones, such as the parabola of a soccer ball or football in mid-flight after being kicked, but I didn't want to just talk about something that everyone can think of and has already expanded on.  I do two sports competitively.  I play soccer, but I also ski race.  Since I already knew of parabolas that occur in soccer, I started thinking, "What parabolas occur in ski racing?"  It took some thinking, but after going through the process of a race, I think I am on to something.

Above is a diagram of a turn of a ski race.  Although there is some information you do not need that is given to you in the picture, it is a good way to illustrate what I am thinking about.  In a ski race, there are alternating colored gates that you have to turn around.  Something that my coach is always talking about is my line.  What line should I take in order to make it down in the fastest time?  The line is a series of parabolas that have origins at each gate.  I think it is very fascinating because each individual racer creates their own individual parabolas as they turn their skis around the gate.  I never thought about how math applied to ski racing, and I think it is very fascinating :-)