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The Toy Story Theorem: Ep. 4


pegkowalski

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In the spectacular finale to Buzz Lightyear's famous 'flight,' he lets go of the ceiling fan to free fall onto Andy's bed.

Please. Consider the following:

In my previous attachments, I used practical numbers, but not that would launch Buzz up to grab ahold of a ceiling fan 7m above the ground (which is the average height of a bedroom). So bare with me as we use that as his starting position now and still consider 2.426 m/s his initial velocity. Using the rest of my long-ago decided upon heights, I will now find Buzz's final achieved velocity before he sticks the landing in front of all the other toys.

Tangentially, Buzz will free fall from a 7m height to a 1m height (the bed) ergo a change in height of 6m.

Y-DIMENSION:

y = 6m

Vo = 0 m/s

Vf = 0 m/s

a = 9.81 m/(s^2)

t = ?

X-DIMENSION:

Vo = 2.426 m/s

Vf = ?

a = 0 m/(s^2)

t = ?

To find time, we use the free fall equation in the y-dimension.

t = [(2y) / a] ^ (1/2)

t = [(2(6)) / 9.81] ^ (1/2)

t = (12 / 9.81) ^ (1/2)

t = 1.223 ^ (1/2)

t = 1.106s

Now we have, in the x-dimension:

Vo = 2.426 m/s

a = 0 m/(s^2)

t = 1.106s

And as an equation we know that:

Vf = Vo + at

So plugging in...huh. Acceleration will again cancel out. So the final velocity will AGAIN equal the initial. 2.246 m/s? Or at this point - really ANY velocity you end up with, based on actual measurements, will tend to remain generally constant over the course of Buzz Lightyear's crazy journey!

Yet, we can put it all together and realize that this entire journey still did only expanded over the length of one bedroom and a one minute long Pixar scene! So I guess that's more believable than not.

That's distance is 'x.'

x = (Vo) (t) + (1/2) (a) (t^2)

x = (2.246) (1.106) + (1/2) (0) (1.106)^2

x = 2.484 + 0

x = 2.484m

That's it! Four aspects of fzx in 2.484m! But more importantly, four aspects of fzx in Toy Story! And that's all that really matters. To me, anyways :)

"I'm packing you an extra pair of shoes; and your angry eyes, just in case."

~Mrs. Potatohead

Sometimes, I find fzx extremely frustrating and slightly maddening. But it always pays to walk the distance. I guess that's all I've got to say on this childhood classic. But I'm sure I'll be BRAVE enough to examine another Pixar movie, quite soon ;)

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