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$\cdot$ In each of the cases that follow, the components of a vector $\vec{A}$ are given. Use trigonometry to find the magnitude of that vector and the counterclockwise angle it makes with the $+x$ axis. Also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) $A_{x}=4.0 \mathrm{m}, A_{y}=5.0 \mathrm{m},$ (b) $A_{x}=-3.0 \mathrm{km}, A_{y}=-6.0 \mathrm{km},(\mathrm{c}) A_{x}=9.0 \mathrm{m} / \mathrm{s}, A_{y}=$ $-17 \mathrm{m} / \mathrm{s},(\mathrm{d}) A_{x}=-8.0 \mathrm{N}, A_{\mathrm{y}}=12 \mathrm{N}$

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Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

University of Michigan - Ann Arbor

Simon Fraser University

McMaster University

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

07:21

In each of the cases that …

08:23

If a vector $\vec{A}$ has …

10:41

$\cdot$ In each of the cas…

03:26

Find the magnitude and dir…

In each case, the $x$ - an…

06:57

In each of these, the $x$ …

03:03

Use a scale drawing to fin…

09:16

07:18

03:57

Draw each of the following…

05:48

For the vectors$$\vec{…

01:11

For the displacement vecto…

05:09

Okay, so we're doing in chapter one problem for one. So in this problem, they gave us components for about a. They give us the day X and a Y, and they ask us to find the magnitude and the angle the counter clockwise angle it makes with e plus positive X axis. Okay, So for a big buss, a X goes 4.0 meters in a wad of five meters. So if we draw that we have, here's our 45 selector. There is an angle going in to get and we have everything there. Okay, So to get the magnitude, we just take this right triangle into hiring Dear Monnet. So it's right now, Mrs Horse Square plus five squared and we see that is six 0.4 meters cool. And to find five wherever I need to take the car tangent. Since we know the opposite and adjacent of our opposite side, which was five over our Jesus just for and we see this comes out to be one degrees cool we want to be. They give us an axe of negative three condoms with a Y bug negative six copters. So here's negative. Three. Your name is six. This is our A and our five. This big angle here. Okay, so to get this, what's killing the magnitude first this easy one, this is the square root of three square plus X squared is comes out his export 70 kilometers are magnetic. Cool. So for fine, Instead of plugging in the how use with enough air signs, let's plug in just how use itself. And we could just find the link of or the angle of this right triangle. And then we know that the total angle we're looking for is 180 like they're plus that what little of it. So this is 1 80 plus art changing. Oh, six over three amount of three over six. Six over three. When this comes out to me. 243 degrees. Cool. So let's get another page in here. Move on. See, Percy. They give us in a wax off nine meters per second and a Y. They give negative 17. Good. So let's plug that in. Sketch, it says, are nine negative 17. Here's our A and eyes always around here. Good. Hearst is finding magnitude. Adrian. What? Plugging that in our calculator. We get 19 years for second. Cold doesn't always come out simple like that. So for five again, let's just chop this off as a right triangle. We find this thing of value here and we can add what we already know to get to by the state of value is the arc team we're going to use. So we add 2 70 degrees to that. And we have find the art intendant of R y opposite value, which will be the acts in this case. I'll be tricky here. Right. So this is going to be nine over. Name her 17. Unless he calls out to me 298 degrees. Perfect. This immunity they give us in the x of negative eight news. And there it was, anyway, of 12 Nunes. Okay, so we sketch this. This is our negativity. They're 12. Reply. Some of us do They as before he squared plus 12 squared square. Do all that we find. This is 14 Newtons per so now. Jar right. Triangle Here we can add 90 because this year, 90 So we had minded degrees. The most part are opposite value. Here is the X again, which was a little bit weird. We gotta make sure we have to look at our triangle. How we're drawing. It's our opposite. Values are X. That's eight over 12. When we add them together, we get 124 degrees. It's pretty that one's for See Possum.

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