Mallard have an output in continuous flight of ~30 w/kg, and a mass of 1 - 1.4kg, giving ~30-42w mechanical output.

30-42w / (745.7w/hp) ~ 0.040 - 0.056 hp/duck.

400/(0.040 - 0.056 hp/duck) ~7143 - 10000 ducks required.

Sources:

Simple Science of Flight - Tennekes

Readings in animal energetics - Catlett

Wow, awesome! It's curious how close to being accurate they were with it probably being written as a joke haha

This may be my new favorite math ever.

This comes round every few months with a different source, different conversation and often vaguely different numbers of ducks and horses. So by this point they are quite possibly referencing the whole duck power thing when they say "that's 7000 ducks".

So here's the original report on it (the actual journal entry is inaccessible currently) https://www.sciencedaily.com/releases/2013/09/130916110853.htm

So yes, the smallest amplitude of surface pattern that could be distinguished reliably was 13nm.

A human finger is about 1cm across. The world is about 12,742km across. That means the world is about 1,274,200,000x bigger than a finger

13nm * 1,274,200,000 = 16.56m

Which is the height of a 4-5 storey building. Not many houses are that big, but I'm sure there are some.

TLDR it would have to be a bit of a larger house?

Yep, or an apartment building as those are commonly taller

It's not talking about two point discrimination, it's just testing if you were to touch a flat surface with ridges 13nm wide in amplitude and 760nm wide* if it could be sensed. Apparently it was sensed by feeling the vibrations when running your a finger along it. The top comment has more information

Edit: phacts

She forgot to take the interest rate into account.

If she still has 58 years to live, she would break even at an interest rate of 11.5%.

However when taking weekly expenditures in account, the interest rate required to break even in 58 years would be even lower

You'd be best off taking $4k a week. Then apply for a loan of $2m repaid over 30 years. $2,477 would cover your loan repayments (assuming 5% interest, although given the guaranteed income you could probably get it for less). So you can get a £2m payment AND a net $1423 per week.

This is true, I didn't take interest into account because I'm a basic bitch and they didn't teach me that stuff in high school. /: Can you please explain this to me so I can be educated?

Ignoring taxes as they differ depending where you live, if you put $2m in to a bank account it will earn interest. 4% interest would be $80,000 per year income on $2,000,000.

But, you have to factor in compound interest. So if you spent nothing you'd have $2,080,000 after one year. All this attracts interest, including the $80,000 you've just earned. So after ten years, because of compound interest you've got just shy of three million ($2,960,488.57 to be precise). After 20 you've got $4.3m. Einstein called compound interest the eighth wonder of the world. Have a play around with the calculator here: http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php

Now it's unlikely you could go for this period of time without spending any money, so you'd have to factor in how much you would spend and whether it would reduce the interest earned by too much.

As I said, this ignores tax because it's too complicated and specific to one's circumstances and also assumes 4% interest. If you were to invest you could potentially achieve a better return.

First, here's the image with some measurements of pixel raidii of the spheres: (feel free to verify this in paint)

Going by the info on this page: https://en.wikipedia.org/wiki/Water_distribution_on_Earth

Specifically:

The total volume of water on Earth is estimated at 1.386 billion km³ with 97.5% being salt water and 2.5% being fresh water

Now the oceans are actually only 96.5% of the total water volume, according to that page. The rest of the salt water is in rivers, underground etc.

So for oceans:

0.965 * 1,386,000,000 km^3 = 1,337,490,000 km^3 volume of a sphere = 4/3 * pi * r^3 so r = (3 * volume / (4 * pi))^(1/3) [power of 1/3 means cube-root]plugging in the numbers, we get:

r = (3 * 1,337,490,000 km^3/ (4 * pi))^(1/3) ~= 683.5kmThe radius of the earth is 6,371 km on average, so a ball of ocean water would be about 1/10th the radius.

If you look at the image with pixel measurements I linked, the pixel-radius of earth is 318 pixels, so we'd expect the Ocean ball to be around 31.8 pixels - which it actually is!

Now for the fresh water, the math is the same:

0.025 * 1,386,000,000 km^3 = 34,650,000 km^3 r = (3 * 34,650,000 km^3/ (4 * pi))^(1/3) ~= 202.2kmWhich means we'd expect the fresh water ball to be roughly 1/30th the radius of the Earth, or in terms of pixels 318/30 ~= 10 pixels. The actual pixel-radius of the fresh water ball was around 7 pixels - which is pretty much close, considering the bad image quality and how fuzzy the boundary of the small sphere looks.

So, yes, it's a fairly accurate representation of ocean and fresh water.

Just take this upvote.

and they probably want a check ✅

According to a quick Google search the ocean has 1.332 billion cubic km of water which is 1.332 e+18 cubic meters. Converting that to a sphere would net a radius of about 424 miles meaning that sphere would be about 850 miles across. From the perspective of that image I'd say its at least in the ballpark. The freshwater math is a bit more tricky so not sure about that one.

There's not enough information here to solve. I thought if I found the precise location in Google maps I could determine the missing geometry to work it out, but that didn't help either.

Here's the spot:

https://www.google.com/maps/@58.8898913,12.2107286,3a,75y,54.34h,88.19t/data=!3m6!1e1!3m4!1s-sl6ONvwevnl7Qud47wTSA!2e0!7i13312!8i6656

It looks like around 40-50 feet from the ramp to the barn, but there's so much uncertainty in that length, the angle of the ramp, how far along the trajectory the car was when it found the barn, etc. If you factor all of these in you get a range that exceeds the realistic range of speeds that car would be going.

We would get a better answer just picking a number within a certain percentage of the speed limit on county road 172.

Based on this, probably around 110 km/h or 70 mph.

Edit: also fuck this sub for downvoting me for pointing out the simple truth that math can't solve this without knowing the geometry of the problem. I guarantee you'll get a closer answer from the speed limit than from physics if you have to make blind guesses on the slope of ramp and distance to barn.

Edit 2: sorry, maybe that was uncalled for.

Looks about 2 metres up.

Max height is v * sqrt(sin(launch angle) ) /2g

Rearranging: v=height*2g/sqrt(sin(launch angle))

Assuming 30 degree launch angle which means

V=229.8/0.7=56m/s=200km/h=120mph

Less if you assume a steeper launch angle. At 45 degrees it is 46m/s=165kph=100mph

All numbers are approximate because I'm on mobile

Edit: these are minimum speeds because it might not have struck at the top of the parabola. I doubt the angle is more than 45 though.

Edit 2: if it's really 3m height that makes it at least 250 km/h. I suspect that we're looking downhill or something. I doubt that little thing could do more than about 180

Edit 3: ok if you account for ramp height, energy loss from damage, uncertain trajectory and general ass fuckery the speed was probably between the 2 and 3 metre estimates. So I'm calling it at exactly 178.2 km/h because you're not the boss of me.

Edit 4: I was wrong. I am going to blame my staff. Don't worry, they've all been sacked. It should have been

v=sqrt(2gh)/sin(launch_angle) which comes to 40-55 km/h. Thanks to /u/beardmath for breakfast

/r/theydidntdothemathbuttheysureasfuckdidtheirresearch

I reverse Google image search the picture to find a news story saying it was near Billingsfors, Sweden, and then looked along the road for a red barn. Turns out there are a lot of red barns or I would have answered sooner.

Post this over in /sub/kerbalspaceprogram and someone will probably build it in the game's simplified physics engine. With any luck, they'll take it into orbit.

I don't see why it couldn't fly. It's not substantially different from a monoprop style plane. It's a safe bet it wouldn't be efficient, however. If it was, we'd see that sort of design in use. I think the issue would be the extra surface area for non lifting surfaces (the bodies), and the extra weight from the oversized turbine.

Also, it would be fucking terrifying when you hit a little turbulence.

Edit: Turbulence, not turbolens.

Yes indeed. I used KarmaDecay to find it, and here it is, from June 2015.

Question is, is that old aero-model, or new? Because I think someone should do it in the new.

/sub/frugal_jerk might appreciate this

Honestly half a cent per play is more than I'd expect. That's 2000 plays to hit the price of an album. There are several artists that I play ~1,000 times a year according to last.fm, so if we assume a two-year cycle I'm basically buying every album those artists put out in the period I'm listening.

Weirdly there's only one song I've "bought" with 200 Spotify plays since I started last.fm about a year and a half ago.

I guess I'm still screwing over all the other artists I listen to.

Spotify is convenient. If streaming music didn't exist and a artist was relying on me to feed them they would have starved to death a long time ago.

Math requires precious calories.

This question is fallacious. It should be more like "what are the chances ANY Google car would pass ANY Bing car at ANY point in time"...and even that's probably too specific

Not an answer to your question. Here is the picture from the other angle: https://imgur.com/a/hvyqj

Link to Bing Maps Link to Google Maps

Its not like they could pass eachother on different days anyways...

They looked like they have stopped and had a chat, what do you think they talked about?

According to Google, a sword weighs about 3 pounds. That 3 pounds is made of 359 people, meaning each contributes .008 pounds. That's about .0036 kg, or 3.6 grams. Google says that the average person has between 3.5 and 4 grams of iron in their entire body.

So it might not all be from blood, and perfect extraction is obviously an issue, but it seems like the math is surprisingly on-point.

EDIT: As another comment here notes, it seems this actually originally came from a post on this sub.

I already killed the 359 people, no need to downplay the numbers.

It's correct because it's stolen straight from this very site.

...like the math is surprisingly on-point.

Did....did you make a sword pun?!

There's no parabolic path to match a velocity to, it's just a straight line. So the closest answer you're going to get is "fast enough that that it appears to follow a straight path for the distance that it's in the frame of this picture." From the photo I'd say it'd have to go about 300mph to not notice the ballistic trajectory. But again, there can be no definitive answer to this.

Edit: To give everyone a better idea, I plugged in some numbers and graphed the resulting trajectories for a launch angle of 30 degrees and speeds of 150mph (about 70 m/s) and 300mph (about 140 m/s), respectively. Both the x and y axes are in meters.

Notice how at 150mph you can clearly see the curved trajectory, and at 300mph you cannot easily see it.

I'm fairly certain the answer is a million jillion miles per hour. Source: have a kid.

But roller coasters don't just float off the track. We'd also need to know how much force it would take to break off the wheels that run on the bottom of the track.

Not just break off the wheels but to snap them off so abruptly that there is no noticeable jolt or velocity decrease