Dope Tech Episode 2

<<@zachstar says : Hope you guys enjoy! As stated at the end I'll taking a little holiday break so will return in the New Year (possibly with a new skit video). You can check out the second channel https://www.youtube.com/zachstarhimself for exclusively skit videos and as always check out https://STEMerch.com to get the floating globe, meme shirts, and more.>> <<@HesterClapp says : If you can stretch the prison around the great circle of the 4D observable universe then you probably deserve to escape>> <<@patrickperot6296 says : Headwinds, giggity.>> <<@hunterkillerai says : I must admit that I heard that as oily macaroni at first.>> <<@tallskinnygeek says : With a much, much faster wind, the plane can go very quickly from A to B, then take the long way around the planet to get back to A, and decrease the total time.>> <<@xuchris1400 says : Flying through headwind is actually faster than with tailwind since it creates more lift.>> <<@nightfox6738 says : The thing I tend to get curious about for the 2nd one is HOW much faster does the faster boat have to be to be able to catch the slower boat using the spiral? What's the slowest the faster boat can be in relation to the slower boat and still be able to catch it? Also couldn't you just change the base of the logarithm to potentially catch the slower boat with a slower and slower fast boat? Just as long as it IS faster.>> <<@boium. says : Imagine the wind speed w is greater than the velocity of the plane. Then the plane would never be able to travel from B to A, hence the time is infinite. (You can also observe this in the equation as well, if w>v, then t<0 which is absurd)>> <<@dougaltolan3017 says : What if the trawler enters the fog, changes direction, stops.>> <<@adrianperez-martinez6292 says : This happens to me all the time 100%>> <<@johnpipping3848 says : The still air vs constant wind journey scenario can be asnswered much more simply using common sense. With a wind, any tailwind acts to improve groundspeed for less time and the headwing acts to reduce groundspeed for longer.>> <<@yairkaz says : Pretty sure blackpenred pen made a video proving e*pi is irrational.>> <<@topphatt1312 says : As a random thing I can confirm these are random things>> <<@christianwiese9887 says : the trawler problem: how fast must the second boat go (more than 3 times the original speed?) and what shold the helmsman do to the rudder? the latter can be figuered out, but are patrol craft 3 times faster than cocaine runners>> <<@applepiepinefruit7626 says : vsauces 3d visual in the bnach traviski paradox shows better in case anyone intrested, not to disregard Zach stars efforts of course.>> <<@attila0323 says : So how does the boat chase affect my life? Great video tho!>> <<@OneEyedJacker says : The aircraft that flies in windy conditions has to execute its landing approach and take-off into the wind at both airports. It therefore has to fly further that the aircraft flying in no wind. Flying in calm conditions, the aircraft can take-off and land in the direction of its destination on both legs. The calm flight takes less time. Sometimes, there’s more to a problem that meets the eye.>> <<@geraltofrivia9424 says : You can prove the answer to the first question using the harmonic mean.>> <<@ATOM-vv3xu says : this is false: if the wind blows fast enough it will be faster to travel with the wind, since the world is round, so you can just go around the world, its false to assume that we are on a flat earth>> <<@dude_thats_rowin says : wow its good to know that i could become outside of an infinitely stretchy ball in a 4d hyperspherical universe>> <<@DAGIEBOB says : I was binge watching your skits. I genuinely watched 8 minutes of this before i was like, wait, this one isnt a a joke.>> <<@Alex-qq1gm says : I thought this was going to be a video about drag not being symmetrical :-/>> <<@bruce4139 says : I know I'm probably breaking some rules but for the trawler problem cant you just look at the waves the boat creates? Or are we assuming that boats dont create waves?>> <<@louisrobitaille5810 says : 4:12 Animator: So you're telling me my copy-paste skills are *not* mathematically precise? Find yourself a new animator! 😂>> <<@gytoser801 says : 2:30 a/b - a/(b+k) = a/b * k/(b+k) a/b - a/(b-k) = a/b * k/(b-k) difference in b-k term is greater in absolute value.>> <<@andrerenault says : That visual explanation of 0.577 helps me understand statistics a little better. It pops up somewhere in the Gumbel or Pearson distribution and now I have a guess as to why.>> <<@daytradersanonymous9955 says : Pure mathematics( I enjoy math and engineering) is like that kid who says "o your so thirsty even if it's wet? What about gasoline??" 🙄 just doesn't do it for me. Can't stand riddles or technicalities>> <<@LQR1772 says : How does this affect my boat?>> <<@fluffydragon1525 says : But if you take the average (mean)speed of each round trip, it’s equal. (v+v)/2 = 2v/2 = v ((v+w)+(v-w))/2 = (v+v)/2 = v By definition, calculating the time of travel with the average speed is no different than calculating it with each individual speed as a separate term. But idk, I’m just a high school student in physics 1.>> <<@1.4142 says : The plane problem is similar to the doppler effect with a moving source.>> <<@FourthRoot says : Well, if points A and B are on opposite sides of the earth the wind could help in both directions.>> <<@jasonscst says : I know if pi*e is rational or irrational. Let’s take pi to be approximately 3 and e to be well, approximately 3. 3*3=9 which is rational.>> <<@jackhandma1011 says : The solution to the second one is just cool as f*ck.>> <<@samegawa_sharkskin says : 5:34 oily macaroni constant>> <<@LilCalebW says : Nice>> <<@notaninterestingperson5769 says : All hail the great circle>> <<@ukranaut says : Like.>> <<@tc6818 says : 4:55 Spock: "Mr. Star is intelligent, but not experienced. His pattern exhibits two-dimensional thinking".>> <<@rishabhgaud says : How aeroplane fly without air>> <<@kanphotploychinda6195 says : "For this next one it will be completely relatable" "Big boat goes invisible">> <<@Tore_Lund says : Another thing: Wind resistance increases with the cube of speed. As planes are fast, tail wind means very little. That is unless you are in a jet stream, so head wind is always several times worse. Commercial pilots usually hypermile, They fly slower in a headwind, i.e. they don't compensate completely by using the required amount of fuel to maintain speed and also throttles back in a tailwind.>> <<@MitchBurns says : You say that there are many combinations of e and pi that are unknown if they are rational or not, but you don’t mention the fact that e^pi is rational. We know that because e^(pi*i)=-1, and both i and -1 are rational.>> <<@teucer915 says : When transcendental numbers were first proven to exist, nobody knew of a single example for years. There was a conjecture that pi was one, but it wasn't proven. So that number that might or might not be rational is a reminder of that flavor of historical uncertainty.>> <<@tukan1652 says : baloon 4d sphere thing means that every point in closed universe would have it's antipode. Never thought about that>> <<@woutervanverseveld5326 says : 9:10 As a human who has been stuck in an infinitely stretchy baloon withinn a hypersphere, can confirm this works>> <<@tjejojyj says : There is something like the trawler problem that had real world consequences. In the 1980s a Cessna on a delivery flight to Australia lost its compass and couldn’t find its heading. A passenger plane (DC-10, IIRC) was asked to help and agreed try to find the Cessna. Passengers also agreed (and delay the flight) by looking out the windows. However to find the lost plane they first noted when and where they first made direct contact with the Cessna and then had to fly until they lost radio contact. The radio range was well known and they calculated a rendezvous point then guided the plane to safety. It is thought they flew passed the smaller plane but it was so small that it wasn’t spotted. I can’t remember the book I read this in. The Wikipedia entry has a slightly different (and probably more accurate) version. https://en.wikipedia.org/wiki/Cessna_188_Pacific_rescue?wprov=sfti1>> <<@youtubeuser-mc4wy says : at 7:00 what is e?>> <<@bot24032 says : 1. U can think of it like that: you fly with boost for less time than with anti boost>> <<@KerbalLauncher says : The Euler-Mascheroni constant looks suspiciously close to 1/ sqrt(3).>> <<@jwbonnett says : The wind senario doesn't make sense though, headwind gives a plane lift which can make said plane faster! And there is no limit set on the question to how complex the answer can be which means the answer can be either faster or slower.>>