S0704: The Raiders Minimization

I waited to post to see if anyone would find the Easter Egg on the whiteboard of tonight’s show.    It turns out that executive producer Steve Molaro commandeered one of tonight’s whiteboards.  (Well “commandeered” may not be quite the right word for someone who takes what he has full rights to.)

And truth be told I was frightened anyone would ever see it:

For tonight's episode, the producers added a whiteboard of their own to tonight's show.

For tonight’s episode, the producers added a whiteboard of their own to tonight’s show.

If that is not clear enough, then consider the title of this week’s episode.   Now having Mr. Molaro’s permission to finally reveal its  source,  I ask you to look carefully at the critical scene of The Raiders of the Lost Ark.

These equations come from Indiana Jones's class room.  Spot the problem?

These equations come from Indiana Jones’s class room. Spot the problem?

But as impossible as it may seem, it appears the folks at “Raiders of the Lost Ark” must not have had a science consultant — since these equations make no sense. If any of the BBT whiteboards’ dozens of fans had noticed it, they might blame the error on the BBT’s science consultant.

We can tell from the words and symbols this is about projectile motion.  The problem all started when I tried to figure out what that equation must have meant.

In physics we often first understand equations through their units.  The variable h is the height of the projectile and is measured as a length, typically in meters.  That’s no problem with the first factor v2/2g because that has units (meters/second)2/(meters/second2).  Voila meters.  The second factor has two terms.   The first term,”1“, has no units so we are still in meters.  The painful part comes with the next term a2g2/v4.  Put in the units and the meter4 cancels meter4.  So far so good.   But the seconds do not cancel and you are left with 1/(seconds)4.  You can’t add that to something unitless.  And even if you could, it would change the answer from the nice meters for height  something with crazy units: meters/(seconds)4.

So it was to my great relief that nobody found this.   I did not want to have to answer piles of hate mail or endure the scorn of comments on IMDB.   A number of articles have been written about TBBT ruining Raiders of the Lost Ark.  But until now, those people did not know what must be the real reason why.

8 Responses to “S0704: The Raiders Minimization”

  1. eileen daly (@d_mooncat) Says:

    loved it! i’m such a math/physics noob but i totally understood this. now i feel really special… xD

  2. arturoquirantesro Quirantes Says:

    FWIW, I don´t think TBBT ruined Raiders. Amy´s thesis was, Indy was irrelevant to the story. But it wasn´t. Without him the Nazis get hold of the Ark, fine; take it to the island, fine; die, fine; but then the rest of the germans at the sub base would realize their buddies were missing, send a scout expedition, find the Ark and ship it to Germany. Now, whether Adolf uses it to destroy France or opens it and ruins Berlin, the story would be quite different…

  3. Jeff Says:

    (ag/v^2) is in fact dimensionless assuming ‘a’ is a distance which you assumed for the meters to cancel.

  4. pseudospin Says:

    As Jeff says a must be ‘a’ distance. I think the ‘h’ isn’t actually the height either – it’s a horizontal distance. Also, the expression looks like a Taylor expanded square root…

    Ah, I think I’ve got it!

    If you fire a projectile at a 45 degree angle from a position ‘a’ above the horizontal plane then ‘h’ is the approximate horizontal distance travelled.

  5. Anonymous Says:

    Um the seconds cancel just fine. g^2/v^4 = 1/m^2. ‘a’ is in meters, so it’s perfectly dimensionless, as expected. Check your math again?

  6. Lena Says:

    h = height if the highest point in the trajectory
    a = horizontal distance to this point
    V = total speed of the projectile

    mgh = initial mV_vertical^2/2
    Initial mV_vertical^2/2 = mV^2/2 – mV_horizontal^2/2
    V_horizontal = a / time to the top
    time to the top = V/g

  7. SerialShops Says:

    Discovering your blog: very sympathic (a bit complex for me ^^ )

  8. lifepopper Says:

    something like this !

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