The Final Problem

bbcsherlockftw:

dawnofeden:

e1n:

ihaventeateninthreehours:

geniusbee:

nekoconsulting:

lilywinterwood:

digitalhoarder:

BECAUSE I HAVE NO LIFE AND THIS IS REALLY BOTHERING ME…

The prevailing theory on Tumblr on how Sherlock survived the fall was that he managed to land in a laundry truck.

Benedict Cumberbatch is 1.84 meters tall and by using his body you can measure how far from the building he would have had to jump to make it into the truck. Roughly 7.32 meters.

Sherlock is standing on the Pathological Department of St. Bartholomew’s Hospital. Google Street View shows what appears to be Routemaster double-decker buses which are 4.38 meters tall. The building therefore is roughly 14.6 meters.

You can use Pythagoras’ theorem to calculate the distance which is 16.33 meters. FYI: The World Record for men’s long jump is 8.95 meters and that was done with a running start. Sherlock flopped over the edge with no horizontal directional speed. I don’t think it’s possible for the laundry truck theory.

EDIT: how much time he had to “steer” towards the truck while falling.

Time = √ 2(height)/gravity
Time = √ 2(14.6m)/9.8 m/s²
Time = √ 29.2m/9.8 m/s²
Time = √ 2.98 m/s²
Time = 1.73 seconds

Sherlock was falling for 1.73 seconds.

Question: Can you jump off a 14.6 meter building and land in a truck full of laundry 7.23 meters away in 1.73 seconds?

HOLY SHIT MATH AND PHYSICS

THIS IS LEGIT BECAUSE THEY USED MATHEMATICS

YOUR ARGUMENT IS INVALID

I am so bad at math but I appreciate it. This is QUALITY and jeez even visual aids YES THIS IS HOW I SHOULD HAVE LEARNED GEOMETRY

Sorry to burst everyone’s bubble but this is not quite right.

People don’t fall in straight lines, they fall in parabolas. So Pythagoras has nothing to do with this. What we need is projectile motion physics.

The dark red is the path he would actually take.

So using these figures it still takes 1.73 seconds to fall vertically 14.6m with an acceleration of 9.8 ms-1.

But travelling horizontally there is no acceleration or deceleration. To travel the 7.32m to the truck Sherlock would only have to take off from the roof at 4.23 ms-1. (Because of air resistance he may have fallen slower and taken a longer time therefore this number may be even lower). Average human walking speed is between 4 to 6 ms-1 (I couldn’t find an exact number) so for Sherlock to have reached the truck in that time he would only have to step off. By falling the way he did it looks like he didn’t push off but there is actually a lot more horizontal velocity than if he had just stepped so he could actually reach the truck.

Also this explains why Sherlock chose such a tall building. If the height wasn’t as large he couldn’t have made it that distance to the truck.

tl;dr: Sherlock could have made it to the truck without any particular effort. The truck theory is still viable.

I’m going to regret jumping on this, but the Parabola theory above is the correct one.  You don’t fall in a straight line like what the original theory said.

That said, in order to make 7.32m of horizontal displacement, you need 4.23m/s of horizontal speed, which is NOT walking speed.  According to Wikipedia (on Walking), average human walking speed is 3.1mph, or 1.4m/s.  4.23m/s amounts to about 9.5mph, which is a running speed.  If you don’t believe me, get on a treadmill and set the “speed” to 9.5.  I guarantee you’ll be running like hell.

Taking into account air resistance and all that shit, I’d imagine he’d be pretty lucky to be able to land on the truck.  But even if he was that lucky, landing on the back of that truck will really break some shit.  There has to be a more elegant solution to this, although it was really really suspicious that the truck just drove by after a person jumped off the building and landed next to it.

I’m more intrigued by this:

The truck went missing in one scene. Then it reappeared and drove away, but in the following cut, the truck was back to where it was when it first started.

Maybe it was just badly edited.  But maybe…

Well this is a lot to think about…

READ THE ENTIRE ARGUMENT.

So it seems I may have helped to trigger a physics debate by linking to the OP in my Pink Suitcase Theory post. How awesome is that?

We should absolutely be talking about this stuff. We’ve got a long wait ahead, so we need something to pass the time. Why not science? Sherlock would appreciate that.