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The Toy Story Theorem: Ep. 1


pegkowalski

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If one of your favorite movies of all time is not Toy Story, I think you need to re-evaluate some life choices. There is one thing besides its lovable characters, genuinely hysterical puns and intense plot twists that makes this movie a one in a million instant classic, and that is: the fzx!

Pixar's voted most amazing moment is the scene in which cartoon action absolutely takes to the sky as Buzz Lightyear proves his flying skills in the comfort of Andy's room. Of course the scene is immense fun to watch - but even more fun to analyze!

The launch of his flight begins as Buzz steps onto a hot wheels track and rolls down it on one of those adorable little finger skateboards.

Even just this first step is FULL FRONTAL FZX. Conservation of energy plays a major role in this aspect as when Buzz takes off his he has both kinetic and potential energy that remain to have the same sum from the moment he starts on the track as well as the moment he leaves it and begins to soar.

(1/2) m (v1)^2 + m g (h1) = (1/2) m (v2)^2 + m g (h2)

Because Buzz always remains the same mass, the masses can be cancelled out. And because he begins with a velocity of zero, the first term of the equation can also be deemed null and void.

g (h1) = (1/2) (v2)^2 + g (h2)

'g' is the constant for gravitational acceleration, otherwise known as 9.81 m/(s^2) downward. So in order to figure out Buzz's velocity as he takes to the sky (infinity and beyond), all we need are his initial height and ending height.

v = [2(g (h1 - h2))] ^ (1/2)

For the purpose of this example and my next set of blogs, let's approximate that...

h1 = 1.5m

h2 =1.2m

Ergo...

Buzz's velocity off the hot wheels track and into the air would be:

v = [2(9.81 (1.5 - 1.2))] ^ (1/2)

v = [2(9.81)(0.3)] ^ (1/2)

v = [5.886] ^ (1/2)

v = 2.426 m/s

Immediately following his take-off, what goes up must come down; so as Buzz falls (with style) for what I'll call an approximated 0.5m, he eventually hits a bouncy ball and gains his second wind to continue his extravagant flight performance after an impressive elastic collision, which I will evaluate next time!

In the meantime, FZX C students and peer bloggers: always remember to, as Woody once said, "Reach for the sky!"

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