Vectors and 2D Motion: Crash Course Physics #4

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  • Опубликовано: 20 апр 2016
  • Continuing in our journey of understanding motion, direction, and velocity... today, Shini introduces the ideas of vectors and scalars so we can better understand how to figure out motion in 2 dimensions. But what does that have to do with baseball? Or two baseballs?
    ***
    Produced in collaboration with PBS Digital Studios: / pbsdigitalstudios
    ***
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    Thanks to the following Patrons for their generous monthly contributions that help keep Crash Course free for everyone forever:
    Mark, Eric Kitchen, Jessica Wode, Jeffrey Thompson, Steve Marshall, Moritz Schmidt, Robert Kunz, Tim Curwick, Jason A Saslow, SR Foxley, Elliot Beter, Jacob Ash, Christian, Jan Schmid, Jirat, Christy Huddleston, Daniel Baulig, Chris Peters, Anna-Ester Volozh, Ian Dundore, Caleb Weeks
    --
    Want to find Crash Course elsewhere on the internet?
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Комментарии • 874

  • @crashcourse
    @crashcourse  Год назад +19

    We made quiz questions to help you review the content in this episode! Find them on the free Crash Course App!
    Download it here for Apple Devices: apple.co/3d4eyZo
    Download it here for Android Devices: bit.ly/3TW06aP

  • @aruggles
    @aruggles 8 лет назад +921

    I love crash course physics, but you need to show your work. When you give an answer to an equation, please do an animation that shows how you cam to that number. I already know the physics and the math but, I know a younger me would have needed that middle step. Still love this channel and you're doing a great job!

    • @ram010992
      @ram010992 8 лет назад +34

      +Adam Ruggles Yes, yes, yes!! I was a math minor in college and I'm still lost without showing all the work the whole way. I feel like moving the numbers and letter with animation is cool, but I need all my steps listed to show how those changes are happening.

    • @julioequinones
      @julioequinones 5 лет назад +33

      Those are physicists for you. my physics professor was habitual about not showing work and putting summations all over the whiteboard. it looked like an art class. I remember one day before taking physics passing by his class and the door was open I thought to myself I would hate to be in that guy's math class. Then I realized it was the same guy the next semester when I took physics. I look back at it like a rite of passage now lol.

    • @cyberxxxcyberxxx9464
      @cyberxxxcyberxxx9464 5 лет назад +1

      Since you know physics and math I need a help with my homework 😂
      If a ball is thrown upwards with an initial velocity of 120 ft per second how long does it take for it to go 216 ft
      And is it possible for the ball to hit 900 ft

    • @atharvc9543
      @atharvc9543 4 года назад +4

      They especially need to breath

    • @nourghazal296
      @nourghazal296 4 года назад +1

      I think that someone studying kinematics would not need the middle steps.

  • @RuneWarhuus
    @RuneWarhuus 8 лет назад +1410

    Will CrashCourse videos ever feature breathing?

    • @damnage97
      @damnage97 8 лет назад +89

      crash course biology

    • @RuneWarhuus
      @RuneWarhuus 8 лет назад +146

      I meant - will the presenters of CrashCourse ever be allowed to breath? My head hurts after about 1 minute into CrashCourse videos because of the way it is cut. All natural language pauses are cut out to make an ADHD friendly format. Its like being verbally bombarded.

    • @damnage97
      @damnage97 8 лет назад +25

      +Rune Warhuus I know.. it was a joke

    • @RuneWarhuus
      @RuneWarhuus 8 лет назад +10

      +damnage97 :-p

    • @coena9377
      @coena9377 5 лет назад +11

      Pause the video or play it at a lower speed.

  • @britterthecritter4531
    @britterthecritter4531 7 лет назад +263

    Watching this at 12:15 am, I have a physics midterm in 7 hours pray for me

    • @danherrera8846
      @danherrera8846 7 лет назад +3

      5 Secønds øf Fall Øut Chemical at the Discø! Same here...

    • @b0unce805
      @b0unce805 5 лет назад +8

      a year later, an I'm about to take my physics midterm tomorrow... 12 hrs to go

    • @Zanewms
      @Zanewms 4 года назад +4

      @@b0unce805 9 months later, I have an exam in 12 hrs

    • @celeryystick
      @celeryystick 4 года назад +4

      @@Zanewms 3 weeks later, I have an exam in 12 min

    • @kianagouveia4256
      @kianagouveia4256 4 года назад +3

      @@celeryystick 3 months later, I'm currently taking my exam

  • @EugeneKhutoryansky
    @EugeneKhutoryansky 8 лет назад +1027

    The most important question is: Will that rubix cube on the desk be solved before the end of this series?

    • @adammehdi9205
      @adammehdi9205 8 лет назад +21

      +Physics Videos by Eugene Khutoryansky I love your videos!

    • @crashcourse
      @crashcourse  8 лет назад +239

      +Physics Videos by Eugene Khutoryansky prrrrrrrrrrobably not. But, we can all hope, right?
      -Nick J.

    • @steflinden4231
      @steflinden4231 8 лет назад +11

      +CrashCourse get a professional

    • @modap3000
      @modap3000 8 лет назад +4

      +Physics Videos by Eugene Khutoryansky i'll teach her

    • @888SpinR
      @888SpinR 8 лет назад +14

      +Physics Videos by Eugene Khutoryansky I'll be honest, I don't care if it gets solved, I just want it to have maximum area touching the table!

  • @deepwoodsengineering3763
    @deepwoodsengineering3763 5 лет назад +65

    I have to say, Hank's courses are difficult to compete with, but Shini does an outstanding job. You did a good job in the Engineering course as well.

  • @ThatSilverDude
    @ThatSilverDude 6 лет назад +52

    just got done with my first week of college physics and we learned about vectors. Lets just say i was completely lost until i watched this video, thank you so much for the crash course.

  • @freevpnproxy1669
    @freevpnproxy1669 4 года назад +80

    PHYSICS IS EASY
    WHEN TEACHER IS PERFECT.

  • @BlueyMcPhluey
    @BlueyMcPhluey 8 лет назад +345

    I hope that there is another mathematic crash course series that can work as a prequel to this one...

    • @Donthefirst
      @Donthefirst 8 лет назад

      +josh mcgee yes ;D

    • @difajabug
      @difajabug 8 лет назад +2

      +josh mcgee That's maths you learn at the beginning of secondary school normaly.

    • @abs_nobody
      @abs_nobody 8 лет назад +9

      +halveiz you need all of calculus to truly understand physics. Calculus' sole purpose was to do physics you know

    • @savanahblaskvitch7933
      @savanahblaskvitch7933 6 лет назад +2

      @GoldenApple Mind = Blown.... MY WHOLE LIFE'S BEEN A LIE! THAT'S NEARLY SAYING ALL THE MATH WE'VE LEARNED IS SOLELY FOR PHYSICS

  • @thispandaispurple
    @thispandaispurple 8 лет назад +9

    Crash course physics. The only series I can watch 3 time in a row and still scratch my head about.

  • @fatoundiaye6338
    @fatoundiaye6338 4 года назад +126

    me: this is 2D, let me go find something 3D
    Her: Harry Styles
    me: alright, I guess I need to review 2D (:

  • @sheepwshotguns42
    @sheepwshotguns42 8 лет назад +862

    sohcahtoa saved my life in highschool.

  • @charissalee4486
    @charissalee4486 8 лет назад +54

    when you need more than one direction you turn to vectors.
    best advice ever

  • @nataliemccarthy9140
    @nataliemccarthy9140 8 лет назад +401

    Vector! Committing crimes with both direction and magnitude!!!

    • @theguywholovespie2118
      @theguywholovespie2118 8 лет назад +20

      +Natalie McCarthy I FINALLY GET IT!!!!!!!!!!!!!!!!

    • @savanahblaskvitch7933
      @savanahblaskvitch7933 6 лет назад +14

      I THOUGHT OF THIS JUST NOW! I FINALLY GRASP WTH VECTOR MEANT WHEN HE SAID THAT IN DESPICABLE ME!

    • @jioarabit986
      @jioarabit986 4 года назад +7

      OH YEAHHH

  • @crashcourse
    @crashcourse  8 лет назад +490

    27th!!!!

    • @TheScienceVerse
      @TheScienceVerse 8 лет назад

      hi

    • @jaedenrotondo3373
      @jaedenrotondo3373 8 лет назад

      😂that's amazing

    • @josephdonkin3858
      @josephdonkin3858 8 лет назад +2

      Good job!

    • @hendrickdias8366
      @hendrickdias8366 8 лет назад +10

      Will this course go all the way till quantum theory?

    • @jpchevron
      @jpchevron 8 лет назад

      +CrashCourse There's a mistake with baseball example. When you throw the one ball horizontally it takes longer to hit the ground as you've now increased the distance the ball has to travel to hit the ground. As both balls are only falling due to gravity it would be impossible for them to both hit the ground at the same time.

  • @ricearoni06
    @ricearoni06 8 лет назад +33

    I'm keeping up with these just for fun. I took Physics 19 years ago in high school! It's fun to see that while the world has changed, the math has not. It's good to know that I'll be able to help my high school age kids on their Physics homework too.

  • @Hannah-ef7gi
    @Hannah-ef7gi 4 года назад +62

    Just tryna study and she brings up harry styles 😭♥️

  • @brainiacmaniac9
    @brainiacmaniac9 7 лет назад +16

    Female engineers (and engineering students 😉) out here representing in Crash Course Physics!! Dr. Shini's passion is so contagious!

  • @Rosecleer
    @Rosecleer 8 лет назад +9

    The amount of sheer delight I feel having this explained to me in a way I understand is unreal.

  • @notablackbharbie5807
    @notablackbharbie5807 Год назад +4

    She had me at Harry Styles. 0:11
    On a more serious note tho, crash course is amazing, thanks so much for what you do.

  • @johnochube4042
    @johnochube4042 8 лет назад +41

    I have a test on this tomorrow :D

  • @brenohenrique6666
    @brenohenrique6666 8 лет назад +7

    I'm loving this series so weird to get nostalgic about things like vectors or integrals. good for reviewing things too

  • @heaven3706
    @heaven3706 4 года назад +19

    you are amazing!! I understand it’s difficult to go over an extensive amount of information in such a short amount of time. To everyone out there who is confused: I understand you too!! If you want to review the math aspects of the video, I suggest watching some of NancyPi’s videos, since math is her forte. Otherwise, keep pausing these CrashCourse videos and internalizing the info. I know we can do this!! :)♥️

  • @olagressloes
    @olagressloes 7 лет назад +2

    I am very grateful for the work you are doing! Your physics videos have helped me out in my AP Physics class a whole lot! Thank you, and keep up the good work!

  • @rushikaasureshkumar
    @rushikaasureshkumar 7 лет назад +13

    ONE DIRECTION REFERENCE.....OMG..I LOVE THIS ALREADY!!

  • @najarvis
    @najarvis 8 лет назад +120

    hoping that there are a lot more of these before the AP physics C test!

    • @crashcourse
      @crashcourse  8 лет назад +14

      +Nick Jarvis Every Thursday (barring some holidays) for the next year :)
      -Nick J.

    • @najarvis
      @najarvis 8 лет назад +10

      +CrashCourse Well I guess that means 2 more episodes before I have to take it... I probably should start studying on my own. Still, this sure will help people for next year's test!

    • @khanman888
      @khanman888 8 лет назад +4

      +Nick Jarvis this stuff wont help you too much man. This series is pretty bad at explaining physics. You might get the gist of it, which is the point, it's a crash course, but you probably wont be able to do anything complicated with this.

    • @abs_nobody
      @abs_nobody 8 лет назад

      +Nick Jarvis we're barely into AP Physics AB, it's gonna be a long way bud

    • @SamanthaMDavid
      @SamanthaMDavid 8 лет назад

      +Glenn Edwards thanks for the tip it looks like a useful channel. :)

  • @Tundra-ec3ii
    @Tundra-ec3ii 8 лет назад +45

    This series is going to help me soo much in a few years

    • @arturmizuno
      @arturmizuno 8 лет назад +4

      How old are you? 12?

    • @Tundra-ec3ii
      @Tundra-ec3ii 8 лет назад +4

      Artur Mizuno 14

    • @arturmizuno
      @arturmizuno 8 лет назад

      Tundra1232 then, yes it will, a lot. NERDPOWER

    • @omarsharief8101
      @omarsharief8101 8 лет назад +1

      Ummm... I am 12 🤓

    • @Prim3Pursuits
      @Prim3Pursuits 8 лет назад

      +Tundra1232 Haha I like how you think, it's always great to stay ahead of the game.

  • @SoshiroGames
    @SoshiroGames 8 лет назад +7

    Im a 1st year programmer, this really helped me understand how vectors works on a 2d platform. thanks!

  • @spicychickensandwichs
    @spicychickensandwichs Месяц назад

    Loving the way she describes vector math geometry class information. It just interesting to see how much more serious people were in the old day when resources was scarce. Yeah.

  • @JeremyPezmanTaylor
    @JeremyPezmanTaylor 7 лет назад +12

    I'm studying for the MCAT, and my Physics are so rusty this series is so helpful.

  • @david0aloha
    @david0aloha 8 лет назад +1

    I love this whole channel, but these are really great. Please do more physics videos!

  • @MariaAraujo-bj5sl
    @MariaAraujo-bj5sl 6 лет назад +1

    SO HELPFUL for big concepts on the MCAT! thank you so much!!!!

  • @daniellassander
    @daniellassander 8 лет назад +40

    I love this channel and the presenter is awesome! I really hope i get to see more from her in the future!

  • @juliahormayer7255
    @juliahormayer7255 6 лет назад +4

    This video is amazing!! I'm currently studying Physics at university (in Scotland, as a third choice for a year, so just for fun) despite having a pretty weak Physics background (I even took Physics for my final exam but we just never touched on all of these topics in school for some reason), so I often have troubles solving problems because no one has ever taught me the basics and this video is literally everything I missed out on in school 😂😂

  • @coolio227722
    @coolio227722 8 лет назад

    Great video, so much information i learned! Keep em coming

  • @yanthos
    @yanthos 8 лет назад +1

    I list crash course as my tutor source on my college questionnaire. This has helped a ton thank you.

  • @puddycad27
    @puddycad27 8 лет назад +1

    I honestly learnt so much from these videos than all my hours in lecture combined!! Thank you !!

  • @maryco7140
    @maryco7140 6 лет назад +3

    I suggest: What about adding a little quiz at the end of the video or a quiz file at the description to sum up and recap the lesson tackled in the video, which will make the path to mastery a whole lot easier by adding a good amount of application?

  • @zjenji
    @zjenji 8 лет назад

    These are great videos. Very engaging. Well done CrashCourse et al..

  • @jecsouza
    @jecsouza 7 лет назад +2

    I've watched this video just to practice my English and I ended up took an exelent Phisics class.
    Tks!!!

  • @PinkChucky15
    @PinkChucky15 8 лет назад

    Great video, I'm definitely looking forward to the next one :-)

  • @radhikasnair4901
    @radhikasnair4901 6 лет назад

    Love you guys!!!-A great job as usual

  • @butter1619
    @butter1619 7 лет назад

    it's so great yall do this and give it out for free. I'm so bad at physics and this helps a lot and is super easy to follow.

  • @jeronimoolivavelez1299
    @jeronimoolivavelez1299 4 года назад +1

    Excellent Explanation! Thank you very much!!

  • @surya8891
    @surya8891 8 лет назад

    nice video , it cleared doubts about vertical and horizontal components of vectors

  • @HeinzP100
    @HeinzP100 8 лет назад

    Nice for a quick refresher course. Keep up the physics, my brain thanks you.

  • @Pathos312
    @Pathos312 8 лет назад +1

    Thank you for sharing this.

  • @alejandroortiza8685
    @alejandroortiza8685 6 лет назад

    OH MY GAH! Thank you very much! when you explained it seems so easy. You are great!

  • @JB-123
    @JB-123 4 года назад +1

    Such a great video, thank you!

  • @purplepigfarm5391
    @purplepigfarm5391 6 лет назад

    I subbed before the video even got to 1 minute. And that's amazing to say the least. I'm very particular about who I sub to and making sure they make good content. I look on the sidebar and it is loaded with other videos from the same channel on many other things I would like to quickly learn. In 59 seconds I knew I would learn so much from just this 10 min video; way more than the confusing 30 min lecture I just watched from a college professor.

  • @theheadone
    @theheadone 8 лет назад +2

    These were always my favorite problems to solve back in physics :)

  • @TheTariqibnziyad
    @TheTariqibnziyad 8 лет назад +1

    this does refresh my memory a lot!!!

  • @nightodin2547
    @nightodin2547 8 лет назад +1

    Thanks for the video! :) Really helps!

  • @funfactoryhd
    @funfactoryhd 5 лет назад +1

    Nice video. It really helps.

  • @mmkthemusician5254
    @mmkthemusician5254 4 года назад +1

    Even though we being quarantined thanks to this virus, crash course is always their to hepl us learn.
    CrashCourse physics is definitely one of my favorite crash courses

  • @mechailreydon3784
    @mechailreydon3784 5 лет назад +1

    2 hours worth of lectures in 10 minutes... not bad

  • @SirMetalKing
    @SirMetalKing 8 лет назад

    It's funny, I had my first lesson on Vectors today. This should come in handy for revision, thanks!

  • @dinonid1234
    @dinonid1234 8 лет назад +76

    Go Triangles! Vihart is proud!

    • @walavouchey
      @walavouchey 8 лет назад

      XD

    • @ImranZakhaev9
      @ImranZakhaev9 8 лет назад +1

      Candy corn triangles made of candy corn triangles made of candy corn triangles made of candy corn colonels

    • @TheMasonX23
      @TheMasonX23 8 лет назад +2

      +Demellovlogs And vectors! As a game programmer (especially graphics stuff), I use both constantly :)

    • @quprabeats4476
      @quprabeats4476 7 лет назад

      dab

    • @KatherinePierce_81
      @KatherinePierce_81 7 лет назад

      Dinonid123 illuminati confirmed

  • @bellajaid
    @bellajaid 7 лет назад

    OMFG, I've been desperately thinking y'all need a math sequence and it didn't even dawn on me to look up my subjects in your Physics sequence! Geeze, I love Crash Course!

  • @sanatsingh8955
    @sanatsingh8955 7 лет назад

    This program is done in a such a way that even a 13yr(me) old can understand it. It fills my curiosity and I always learn some thing new.

  • @jcmjub
    @jcmjub 8 лет назад +1

    Yayyyyyy finally! Been waiting for this :D

  • @wesleycurrier13
    @wesleycurrier13 6 лет назад +1

    This is gonna be the savior of my AP Physics 1 exam grade

  • @feynstein1004
    @feynstein1004 6 лет назад +1

    Yay vectors. I remember studying them in my physics class almost 10 years ago. Wow, I'm old.

  • @WiseWik
    @WiseWik 8 лет назад +1

    Shini, you are amazing! :*

  • @jedigecko06
    @jedigecko06 8 лет назад +1

    Can't unsee the 'Big Eyed Hanklerfish' on the left.

  • @TrinJeto
    @TrinJeto 7 лет назад

    I FINALLY UNDERSTAND HOW TO DERIVE THOSE TWO KINEMATICS EQUATIONS! THANK YOU BASED CRASHCOURSE!

  • @kenny1jon2B
    @kenny1jon2B 8 лет назад +4

    I may have to watch this multiple times and take some notes haha

  • @AmeekBindra
    @AmeekBindra 8 лет назад +1

    thanks so much!! I finally get vectors after like six months!!

  • @whitemamba2049
    @whitemamba2049 7 лет назад

    Good stuff. Am utilizing this to better understand Physics and my study of Astronomy/ Cosmology. Also questioned the 2 balls hitting the same ground and remember testing this with throwing and dropping a tennis balls out of an elevated window at the same time (makes it easier to see/ hear them hit as same time) Think the key is that the thrown ball has to be thrown at from the same height as the ball you drop simultaneous with it. If you throw the ball up in any way/ or down, you change this and the balls would not hit at same time. This would explain why we can ignore the horizontal motion/ velocity etc and gravity constant would be only thing that would be acting on the balls (in a vacuum)
    Wonder how this in a simplistic way would explain objects moving at a high speed (near speed of light) or "falling" in orbit around curved space time around planets, suns etc and even the effect on time, but that is another lesson, and I need to brush up on my Newtonian physics first hahaha.

  • @TheGoldenBoo
    @TheGoldenBoo 8 лет назад +11

    I'm really digging how interactive Crash Course is getting with the comments in this series.

    • @justintaylor4614
      @justintaylor4614 8 лет назад

      simple topic made complex

    • @TheGoldenBoo
      @TheGoldenBoo 8 лет назад +1

      Justin Taylor I fail to see the relation between what I said and what you responded to what I just said.

    • @BlackCat-zp6qb
      @BlackCat-zp6qb 8 лет назад

      +Fallenshadowv3 I agree with you i don't get his point either XD

  • @bru513
    @bru513 6 лет назад

    watching it in 2017. You make Physics fun!!!

  • @maithajamal9289
    @maithajamal9289 7 лет назад +1

    Thanks for the video

  • @theTABmail
    @theTABmail 7 лет назад +19

    Who else noticed harold cycling away on the table at 0:02?

  • @JustLoco100
    @JustLoco100 Год назад +1

    The only direction the vectors have sent me to is DEPRESSION ✨
    Lol but thank u sm for this, easy to understand and made me actually learn the damn vectors.

  • @frzferdinand72
    @frzferdinand72 8 лет назад +3

    When I return to college, you're gonna be the real MVPs.

  • @ayad6564
    @ayad6564 4 года назад

    thanks a lot......i have a test tomorrow, crash course saved my day!!!

  • @alinisugly
    @alinisugly 6 лет назад

    Love physics already. Started loving it at 0:11

  • @arunitbaidya6118
    @arunitbaidya6118 8 лет назад +1

    thank you so much do finally doing physics

  • @jincyquones
    @jincyquones 8 лет назад +1

    Vectors are my favorite!

  • @calseed
    @calseed 7 лет назад

    I believe every science learner should watch this video before tackling projectile motion/ Kinematics ..
    This was really helpful , thanks !

  • @DanielDogeanu
    @DanielDogeanu 8 лет назад +718

    I'm sorry, I can't concentrate on the girl with all this beautiful physics...

    • @abs_nobody
      @abs_nobody 8 лет назад +51

      +Daniel Dogeanu good, you'll need that kind of distraction. That's the right kind of distraction

    • @KatherinePierce_81
      @KatherinePierce_81 5 лет назад +25

      I’m sorry I can’t concentrate on the video after seeing a comment from this handsome boy

    • @cheshire__kat
      @cheshire__kat 4 года назад +7

      LMAOO

  • @thatomofolo452
    @thatomofolo452 8 месяцев назад +1

    Thanks for helping me with my homework👍👍😁

  • @cec6607
    @cec6607 8 лет назад +1

    These are my uni classes resumed in a video right here.

  • @McRuffin
    @McRuffin 8 лет назад +31

    Vector! The evil supervillan from despicable me

  • @user-pv3hu1kq1u
    @user-pv3hu1kq1u 8 лет назад +1

    crash course, you blow my mind

  • @trollerjakthetrollinggod-e7761
    @trollerjakthetrollinggod-e7761 8 лет назад

    There's litterally nothing I could find online about vectors, but this makes it pretty simple.

  • @sorrowsfromeden
    @sorrowsfromeden 7 лет назад +1

    This saved my Physics mark thank you so much 😃

  • @TschimmiCash
    @TschimmiCash 8 лет назад

    very nice! thank you!

  • @thetruth3112
    @thetruth3112 7 лет назад +1

    thank you so much

  • @uiopy1
    @uiopy1 8 лет назад

    Oh my god, awesome reference to The Witness you guys... Bravo!

  • @aarushprasad9257
    @aarushprasad9257 4 года назад +2

    When Shini starts talking about vecors and how to add/subtract them, isn't it very similar to graphing complex numbers with I = Re and J = Im? (and the direction is the argument)

  • @malikad41
    @malikad41 7 лет назад +1

    Wish I had such teachers!

  • @itskathyaaaa
    @itskathyaaaa 8 лет назад

    thank you so much!!

  • @teehuynh1198
    @teehuynh1198 7 лет назад

    AMAZING !!! Thanks :)

  • @appa609
    @appa609 8 лет назад +1

    Good job.

  • @Malidictus
    @Malidictus 8 лет назад +1

    Next time should be quite interesting, since I have a sneaking suspicion that we'll get to calculating a ballistic arc and why 45 degrees gets you the longest distance.

  • @photophone5574
    @photophone5574 4 года назад +7

    When you have magnitude and direction. You just got vectored!

  • @theotherVLF
    @theotherVLF 5 лет назад

    Nothing can ever be simple. That's what makes it fun.

  • @manvichauhan3020
    @manvichauhan3020 7 лет назад +6

    That moment when you're watching this in panic mode before a test

  • @TheFireflyGrave
    @TheFireflyGrave 8 лет назад +1

    This series is really starting to hit its stride.