Quadratics: A Story of Freedom and Constraint

When I was younger, I always wished I could fly. I wanted to be able to take to the skies to escape at times, and other times I wanted to fly towards some exciting yet far off event. Grounded? Nope, I'm going up into the clouds! Kevin is having a sleep over at his house Friday night? I know how I'm getting there!

Some say NASA was started by someone who was running from his mother's broccoli.

What I really wanted was freedom. Freedom to do what I wanted whenever I wanted, consequences be damned! I looked up and saw birds flying around the sky and yearned for that ability. I'm sure everyone has felt that urge in their life, and I'd bet it was a driving force that took to the Wright Brothers from their bicycle shop to the shores of North Carolina.

Nowadays, I spend most of my time working with math equations and science theories. One of the first lessons that is taught in physics is learning how to deal with projectiles. An object is thrown into the air from an initial height with a velocity and angle of velocity. It seems insufficient, but that information is all that is needed to explain the flight that object is about to embark on. You see, once the object is flying through the air, the only force acting on it is gravity, so a parabola can perfectly describe the motion of the projectile.

You take that acceleration, add some velocity, throw in an angle. Baby you've got a stew going!

Using the standard form of a parabola, it is very easy to relate this information into a mathematical equation. Using the form ax 2 + bx + c, a is half the acceleration, b is the initial velocity, and c is the initial position. From here, all the rules of quadratics apply. You can convert to vertex form, you can find the roots of the equation, and you can even find the focus point of the parabola.

There is an inherent dichotomy in using parabolas and quadratics to explain projectile motion. This act, seen by everyone person who has ever lived as ultimate freedom, is coincidentally constrained. It is the opposite of freedom! It turned out that my visions of flying freely through the air could not have been more predetermined.

The laws of science and math, which I have spent the majority of my life studying and pursuing, de-mystified one of my dreams. Life, it seems, has it's own sense of irony.

The Far Side - Gary Larsen