The hole to hell or "poor flashlight" [closed]

Question

I try my luck over here

Warning: This was a fun question for some, not for others. And now I know, I should have posted it in the physics forum :-)

At the end of Daredevil (the tv-series) S02E07 "Semper Fidelis", our hero "borrows" a flashlight from Elektra and drops it in the seemingly bottomless pit. I try my luck over here:

I counted 19.8 seconds before the cut to the end titles. The next episode begins and red estimates

Daredevil: "It's gotta be 40 stories, at least."

As a real geek, that got me thinking and I tried to estimate the minimum depth of the hole.

As it turns out, the whole calculation seems trivial, if completely ignoring the fact, that they breathe air. Somewhere around 2km, I guess. Waaay more than 40 stories.

On the other hand (assuming that the super-power of not needing air to breathe is not a hidden plot device), the actual calculation with air resistance, based on the time given to impact, is quite untrivial. There are all kinds of factors involved and from air temperature to object mass, nearly everything matters (physically) and the maths behind it involves evil things like integration.

Enough said. Show me what you got, My humble calculations gave a minimum depth of

close to 500 meters.

That would make 12.5 meters per story. So we are talking cathedral here.

My question to you is:

How would you come up with a minimum depth?

I will share the whole process about getting to the 500m gladly, but this question is more about how you would approach this riddle, so I would consider it a meta-spoiler. And maybe you can save the character of Daredevil from becoming a math-genius too, which would IMHO totally save the day.

Clarification: This question is not about a potential plothole, or the writing or the totally awesome ninja fighting in front of a huge whole. Consider it recreational TV-math... or something ;-)

Answer 1

I had the same problem when that happened. Nerd brain was thinking that was a super, super deep hole, and then he said forty stories and it created a small cognitive dissonance.

My napkin calculations came up with about 800 meters. I used:

Acceleration: 9.8 meters per second
Reach Terminal Velocity at 5 seconds
Falling at Terminal for 14 seconds after that

4.9 * 5^ 2 = 122.5 meters in the first five seconds, plus 9.8 * 5*14 = 686 meters in the last 14 seconds for total of 808.5 meters.

The 9.8 is pretty close, though of course not 100%, variances for wind resistance and the specific gravity of new york, but close enough for doodling while binge-watching the show. :)

Terminal Velocity I just guessed.

But yeah, a lot deeper than 40 stories. In the end, I assume DD is correct for In-Universe Reasons. But it did make me wonder for a bit.

Answer 2

Well, he did say at least. So it could be much more than 20 stories. 21, maybe 22 even. He's the best type of correct. Technically correct.

But it's obviously an inconsistency. A story is typically 10 to 15 feet, or 4~5 meters. So 40 stories would be 200 meters. And our sightless wonder can't see the light, so he's using his fire sense, listening to it in the wind or when it hits the floor something, so we can't expect him to be 100% accurate.

The scene was purely to draw suspense and it worked until you nitpicked at it. You can't expect cinematography to take a back seat to technical realism.