Le Pont de Javert

I was obsessed with Les Misérables when I was a kid. I still had the Zeppelin posters, and my first CD was Black Crowes' Shake Your Money Maker. But that didn't stop me from wanting to be Gavroche, the little Parisian kid who brags about what "little people can do" before outing Javert as a spy.
Richmond. Broadway. Community theater. No matter where I saw it, Les Mis was always le perfect.
Until I noticed this. In one of the final scenes, the French officer Javert jumps off a bridge, presumably into the Seine River below. As he falls, he sings.

If you listen carefully, you'll notice that Javert is falling for a very long time. So you gotta wonder: how tall was the bridge??!
You may remember from high school that all objects fall at the same rate, no matter the weight (and ignoring wind resistance).

We can use this to come up with an equation to predict how far an object will fall over time. The key is in realizing that each distance is a perfect square: after 1 second, an object will fall 4^2 feet; after 2 seconds, 8^2 feet; 3 seconds, 12^2 feet. To find the distance, we simply have to take the number of seconds, multiply it by four, and square the result:

d(t) = (4t)^2 = 16t^2.

According to the song, Javert fell for eight seconds, meaning the bridge must have been (16)(8^2) = 1024 feet tall. To put this in perspective, the Golden Gate Bridge is only 200 feet, while the Eiffel Tower is 1063 feet!
It gets even crazier when you ask, "How fast was Javert traveling when he hit the water?" To answer this, we can create a table to estimate the speed over various time intervals.

From this, we see that Javert would have been traveling between 240-272 feet per second, or 160-185 mph, when he hit the water. (If the actor could have held the note for 27 more seconds, he would have broken the sound barrier...and probably won a Tony, too.) With a little calculus, we can be even more accurate:

s(t) = 32t = 32(8) = 256 ft./sec. 

Of course, this whole scenario is a bit absurd.

If we assume that the average Parisian bridge to be 30 feet tall, then Javert would have really fallen for

d(t) = 16t^2
30 = 16t^2
1.875 = t^2
t = 1.37 seconds

at a speed of s(t) = 32t = 32(1.37) = 44 ft./sec., or around 30 mph. In other words, perhaps it should have looked like this:

In the end, maybe community theater actors aren't worse singers than their Broadway colleagues. Maybe they're just better mathematicians!

6 thoughts on “Le Pont de Javert”

  1. Our class loved Les Misérables so much that our French teacher let us watch it twice. Asking how tall the bridge is as you pose here is so much more intriguing than anything a textbook can offer. Will definitely file this (and Matt's Scott Pilgrim) away for next year. Thank you!

  2. I enjoyed the personal story you attached to this. I find that whenever I tell bits of personal stories related to something, even if the story is stupid or uninteresting, the kids are instantly hooked!

  3. There is one other possibility that could potentially have an impact on your variable (t) or time: Like when we are visiting the dream world, when we die we are no longer bound by the laws of time (theoretically speaking of course). A dream which lasts only a few seconds, for example, can feel like hours or even days in the dream state. If this bloke took his own life, his song may have taken place, in part, on his journey to the place we go after leaving our bodies. The disconnect from the time/space continuum could, in theory, allow him to finish his song. But who would hear it?

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