How Far Did Javert Fall?

In which I answer a question posed to me via a webpage...

This post will be in the style of What-If XKCD without the awesome diagrams and scroll-over text.

So a good friend of mine recently posed the question "How far did Javert fall?" by the medium of this webpage: http://www.mathalicious.com/lesson/the-fall-of-javert/. I clicked on the webpage expecting an entertaining answer to the question but sadly found it was actually an exercise left to the reader. I realise this is a lesson plan but humour me.

Calculating the time taken for Javert to fall is easy. He holds the note in the musical for 8 seconds. Assuming no air resistance and using this formula:

You find he fell 313 metres. This doesn't account for terminal velocity. If we assume human terminal velocity is around 125 mph, Javert will reach this velocity 5.7 seconds into his fall. The final 2.3 seconds are at constant velocity so a better guess of the distance fallen is 288 metres. If you have an unnecessary desire for accuracy it is 287.87 metres. Any astrophysicist will tell you that all of these distances are effectively 300 metres.

So could Javert have fallen this far off of a bridge as depicted in the musical? The short answer is: No. The long answer is, of course, more interesting so allons-y!

So are there any bridges 300 metres high above the Seine? In the book Javert jumps off of the Pont au Change in Paris. This bridge looks to be about 5 people high from the image on the Wikipedia article so around 9 metres above the water level. Even if the Seine was completely drained this would max out at around 16 metres.[1] Clearly we must search for a higher bridge!

A quick Google for "highest bridge in Paris" will tell you that the Pont Mirabeau was the highest bridge built in Paris during the 1800s but sadly after the events of the story. It also doesn't look much taller than the Pont au Change. Frankly we are going to have to look for something taller. How tall is Notre Dame? Tall enough? No at 96 metres even the spire is not tall enough.[2] Javert would have had to wait until the Eiffel Tower was completed to die so dramatically.[3]

The film is no better. It looks like he falls for about 5 seconds: