So far, we’ve spent a lot of time predicting

movement: where things are, where they’re going, and how quickly they’re gonna get there. But there’s something missing — something

that has a lot to do with Harry Styles. And today, we’re gonna address that. We’ve been talking about what happens when

you do things like throw balls up in the air or drive a car down a straight road. That kind of motion is pretty simple, because

there’s only one axis involved. The car’s accelerating either forward or backward.

The ball’s moving up or down. There’s no messy second dimension to contend with. But this is physics. We may simplify calculations

a lot of the time, but we still want to describe the real world as best we can. And in real life, when you need more than

ONE DIRECTION, you turn to vectors. [Theme Music] Let’s say we have a pitching machine, like

you’d use for baseball practice. We’re going to be using it a lot in this episode,

so we might as well get familiar with how it works. We can feed the machine a bunch of baseballs

and have it spit them out at any speed we want, up to 50 m/s. The pitching height is adjustable, and we can rotate it vertically, so the ball

can be launched at any angle. It also has a random setting, where the machine picks the speed, height, or angle of the ball, all on its own. Suddenly we have WAY more options than just

throwing a ball straight up in the air. And now the ball can have both horizontal

AND vertical qualities. At the same time. Before – we were able to use the constant

acceleration equations to describe vertical or horizontal motion — but we never used

it for both at once. And, we’re not going to do that today either. Instead, we’re going to split the ball’s motion

into two parts — we’ll talk about what’s happening horizontally and vertically, but

completely separately. And we’ll do that with the help of vectors. Vectors are kind-of-like ordinary numbers

— which are also known as scalars — because they have a magnitude, which tells you how

big they are. But they have another characteristic, too:

direction. Previously, we might have said that a ball’s

velocity was 5 meters per second, and — assuming we’d picked DOWNWARD to be the positive

direction — we’d know that the ball was falling down, since its VELOCITY was positive. In other words, we were taking DIRECTION

into account, but we could only describe that direction using a positive or a negative.

So we were limited to two directions along one axis. But vectors change all that. Now – instead

of just two directions, we can talk about ANY direction. It might help to think of a vector like an

arrow on a treasure map. You could draw an arrow that represents 5 kilometers on the

map — that length would be the vector’s MAGNITUDE. But you need to point it in a particular direction

to tell people where to find the treasure. Which is actually pretty much, how physicists

GRAPH vectors. You take your two usual axes, aim in the vector’s direction, and then

draw an arrow, as long as its magnitude. Like, say your pitching machine launches a

ball at a 30 degree angle from the horizontal, with a starting velocity of 5 meters per second. We can just draw that as a vector with a magnitude

of 5 and a direction of 30 degrees. And let’s say your catcher didn’t catch

the ball properly and dropped it. Then just before it hits the ground, its velocity

might’ve had a magnitude of 3 m/s and a direction of 270 degrees, which we can draw

like this. That’s why vectors are so useful: You can

describe any direction you want. But there’s a problem, one you might have

already noticed: You can’t just add or multiply these vectors the same way you would ordinary

numbers, because they AREN’T ordinary numbers. To do that, we have to describe vectors differently. When you draw a vector, it’s a lot like

the HYPOTENUSE of a right angle triangle. The vector’s magnitude tells you the length

of that hypotenuse, and you can use its ANGLE to draw the rest of the triangle. Right angle triangles are cool like that: you only

need to know a couple of things about one, like the length of a side and the degrees

in an angle, to draw the rest of it. It’s all just trigonometry, connecting sides

and angles through sines and cosines. Which is why you can also describe a vector

just by writing the lengths of those two other sides. In fact, those sides are so good at describing

a vector that physicists call them its components. So let’s go back to our pitching machine

example for a minute. We said that the VECTOR for the ball’s starting velocity had a magnitude

of 5 and a direction of 30 degrees above the horizontal. We can draw that out like this.

That’s all we need to do the trig. The length of that horizontal side, or component,

must be 5cos30, which is 4.33. The same math works for the vertical side,

just with sine instead of cosine — so we know that the length of the vertical side

is just 5sin30, which works out to be 2.5. So our vector has a horizontal component of

4.33 and a vertical component of 2.5. In what’s known as unit vector notation,

we’d describe this vector as v=4.33i + 2.5j. The arrow on top of the v tells you it’s

a vector, and the little hats on top of the i and j, tell you that they’re the UNIT

vectors, and they denote the DIRECTION for each vector. i just means it’s the direction of what we’d

normally call the x axis, and j is the y axis. You’ll sometimes see another

one, k, which represents the z axis. And if we wanted to add or subtract two vectors,

that’s easy enough — we just separate them each into their component parts and add or

subtract each component separately. So 2i + 3j added to 5i + 6j would just be 7i + 9j.

And -2i + 3j added to 5i – 6j would be 3i -3j. Multiplying by a scalar isn’t a big deal

either — you just multiply the number by each component, so 2i + 3j times 3 would be

6i + 9j. The unit vector notation itself, actually

takes advantage of this kind of multiplication i, j, and k are called unit vectors because

they’re vectors that are exactly one unit long, each pointing in the direction of a

different axis. So when you write 2i, for example, you’re just saying: take the unit vector i and make it twice as long. But it’s NOT the same as multiplying a vector

by another vector — that’s a topic for another episode. So now we know that a vector has two parts:

a magnitude and a direction, and that it often helps to describe it in terms of its components. And when you separate a vector into its components,

they really are completely separate. In other words, changing a horizontal vector

won’t affect its vertical component, and vice versa. And we can test this idea pretty easily. Let’s say you have two baseballs, and you let go

of them at the same time from the same height. But you toss Ball A in such a way that it

ends up with some starting vertical velocity. With Ball B, it’s just dropped. In this case, Ball A will hit the ground first

because you gave it a head start. Now, what happens if you repeat the experiment,

but this time you give Ball A some HORIZONTAL velocity and just drop Ball B straight down?

Which ball hits the ground first? It’s kind of a trick question, because they

actually land at the same time. It doesn’t matter how much starting horizontal velocity you give Ball A — it doesn’t reach the ground any more quickly, because its horizontal motion vector has nothing to do with its vertical motion. With this in mind, let’s go back to our

pitching machine, which we’ll set up so it’s pitching balls horizontally, exactly

a meter above the ground. Then, we get out of the way and launch a ball,

assuming that “up” and “right” each are positive. How do we figure out how long it takes to hit the ground? That’s easy enough — we just completely

ignore the horizontal component and use the kinetic equations the same way we’ve been

using them. In this case, the one we want is what we’ve been calling the displacement curve equation — it’s this one. We just add y subscripts to velocity and acceleration,

since we’re specifically talking about those qualities in the vertical direction. Now we can start plugging in numbers. The ball’s displacement, on the left side

of the equation, is just -1 meter. There’s no starting vertical velocity, since

the machine is pointing sideways. And the vertical acceleration is

just the force of gravity. Now all we have to do is solve for time, t, and we learn that the ball took 0.452 seconds to hit the ground. Its horizontal motion didn’t

affect its vertical motion in any way. But sometimes things get a little more complicated

— like, what about those pitches we were launching with a starting velocity of 5 meters

per second, but at an angle of 30 degrees? Well, we can still talk about the ball’s

vertical and horizontal motion separately. We just have to separate that velocity vector

into its components. Just like we did earlier, we can use trigonometry

to get a starting horizontal velocity of 4.33 m/s and a starting vertical velocity of 2.5

m/s. Now we’re equipped to answer all kinds of

questions about the ball’s horizontal or vertical motion. Here’s one: how long did it take for the

ball to reach its highest point? We already know something important

about this mysterious maximum: At that final point, the ball’s vertical

velocity had to be zero. That’s because of something we’ve talked

about before: when you reverse directions, your velocity has to hit zero, at least for

that one moment, before you head back the other way. So, in this case, we know that the ball’s

starting vertical velocity was 2.5 m/s. And we know that its final vertical velocity,

at that high point, was 0 m/s. Finally, we know that its vertical acceleration

came from the force of gravity — so it was -9.81 m/s^2, since up is positive. And we’re looking for time, t. Fortunately, you know that there’s a kinematic

equation that fits this scenario perfectly — the definition of acceleration. By plugging in these numbers, we find that it took the ball 0.255 seconds to hit that maximum height. So, describing motion in more than one dimension

isn’t really all that different, or complicated. You just have to use the power of triangles. In this episode, you learned about vectors,

how to resolve them into components, and how to add and subtract those components.

We also talked about how to use the kinematic equations, to describe motion in each dimension

separately. Crash Course Physics is produced in association

with PBS Digital Studios. You can head over to their channel to check out amazing shows like The Art Assignment, The Chatterbox, and Blank on Blank. This episode of Crash Course was filmed in

the Doctor Cheryl C. Kinney Crash Course Studio, with the help of these amazing people and

our Graphics Team is Thought Cafe.

Hello Dr. Beautiful 😍😍 I think I'm in love.

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.

why is it that only the crash course physics person is the worst at explaining ideas

can someone summarize the video?

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

Does this playlist suitable for IGCSE ?

I’m sorry but this doesn’t explain vectors very well at all and even at most points doesn’t explain it

She said 'the power of triangles…' ILLUMINATI CONFIRMED

🙁

This video makes me dizzy with the switching focuses and Shini's choppy fast prattling. It keeps cutting out yet the producer attached a new clips without a pause…no breaths for Shini. It's weird and cannot be good for anyone's concentration. What kind of filming technique is this? I spent more time trying to figure out the filmography than listening to the video. This cannot be for real.

SHE SAID HARRY STYLES AND I CHOKED OWNHDJSD MY BABY

Did she just make a 1D pun-

you r so goddamn hotttt

Harry Styles in Physics Lecture was the last thing I expected.

850th!Harry styles..💗

this helped a lot thank you so much!

AP rest on Tuesday and I know nothing

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

This had nothing to do with Harry Styles🤔😅, very helpful video though I finally understand vectors.

"5 cos 30" lmao

Man. She is beautiful and intelligent.

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

base ball? I'm in Australia.

pitching?

Crash Course Is The Best!!😀

a train moving with acceleration of 5 m/s^2 have 1 engine of mass 100 kg and 4 coaches of mass 50 kg each find the force exerted by 3rd coach on 4th

pls help me

it also involves vectors

Why not just plot a graph, use the integral and then find the velocity.

I suppose it will be easier.

I use this method all the time.

Why factor not in ""weight" of the object?..

how many dimensions is the motion of tilting on a pivot ?

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

Can you add Swedish subtitle to this videoes please , it would help alot

I cannot find lesson 2 and 3

Doesn't the balls horizontal distance affect the time it takes because lengthens the distance of the drop at

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

Can anyone explain to me why did we choose the vertical velocity and the gravity turned negitive?

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?

Every machinist who watched this had an aha! moment at the I/J/K part for X/Y/Z lol

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

h-harry styles

I’m dumb

Anyone here because they don't understand the homework?

For as much as I don't like sig figs they surve a purpose

But isn't gravitational acceleration taken as negative always if up is taken to be positive , since it acts downward

hi i have my physics midterm tomorrow and i'm gonna die lololol

2:22 Somebody at PBS digital studios likes The Witness

Harry styles stole my attention…!!

Can u replace my physics teacher?!!

This is extremely boring

Some of us don’t understand trigonometry

AAAAAAAAAAAAAAAAAAAAAAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH. good lesson, really helped me understand the maaAAAAAAAAAAATTTTTTHHHHHHHHHHHHHHHHHHHHHHhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhHHHHhHHHhh

Vectors : اشعة

*intense music plays after ~The power of Triangles 🔺~

zee ;D 4:54

I stayed because I heard Harry styles

ONE DIRECTION

What does this have to do with Harry Styles?

Okay, so in the last problem that they give (what was the maximum height of the ball?), why did they have to go backwards? Also, if the force of gravity (g), was negative, how did time end up positive. FYI, I'm currently completing Alg2/Trig so it's been a confusing couple of episodes.

I don't understand?

Nice video. It really helps.

Her hair is so pretty im jealous

i am a fan of crash course, but i think a lot of episodes in this series weren't written well.

Took me an hour to note this video

Physx is easy

I didnt understand when she used trigonometry like sine and why or HOW she used them. Can anyone explain?

2 hours worth of lectures in 10 minutes… not bad

Only useful for those who already had studied vectors and scalars

Not bad….

But she needs to be a bit slowwww…..

AP Exam tomorrow

At time 6:30–6:49) My intution says the balls would hit the ground at the same time. But since I was a teen I guess I had difficulty in separating motion in more than one dimension and would think Ball A and B travel at the same acceleration/speed and reach the ground at the same time yet Ball A had traveled a greater distance than Ball B!!!!

Vector is not the same with scalar because vector has direction and magnitude.

WHERE DO YOU GET 2.5 AND 4.33??????????????????????????😠

If you are still in school play video at 0.5x. If you are in college, play the video at 1.5x. For most people videos in this serie are too fast, or too slow…

Algebra > Geometry > Triganometry = Calculus

Can u teach me cape physics (advance)

OOhhhhhhh, Harry Styles- 1Direction……. SO LAME XDXD

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.

For the first time in my life, i understood physics. More specifically everything she said after Harry Styles. 😛

Wow! Thank you.. I just proved how I suck so bad at physics! I still don't get it 😂😂😂😂

Oh that's really crash course …

hArry styles and one dirEctiOn, dude i’m okAy

What is the difference between Vy and V0,y

you people say z as zed instead of zee? What do you call a zeebra, a zedbra?

3D motion video also

I want that accent!

semma mokka

me: this is 2D, let me go find something 3D

Her: Harry Styles

me: alright, I guess I need to review 2D (:

Just learned 2D motion in pre-AP Physics in high school, wanted crash course to clarify some things

i'M sTilL c0NfuSeD aFwhat has this got to do with Harry Styles

who tf are you

You made physics look beautiful to me. never found it interesting until now

Thank you jesus

Qualify the motion discussion with "in a vacuum". In particular with the pitching analogies, assume no curve balls or sliders.

directioners anyone??😂😅

Totally Cbse class11 Course it is…

Cbse is the of Indian Government ..

I'm getting a lot of help from ur channel . smart teaching way..

I LITERALLY SCREAMED WHEN SHE SAID HARRY STYLES

Creepa

What