Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Compute the $x$ and $y$ components of the vectors $\vec{A}, \vec{B}$ and $\vec{C}$ shown in Figure 1.24

A) 9.6B) $-9.6$C) $-3 \sqrt{3}$

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Cornell University

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

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.

06:10

Compute the $x$ and $y$ co…

04:35

Compute the $x$ -and $y$ -…

05:40

Compute the $x$ - and $y$ …

03:52

Compute the $x$- and $y$-c…

01:39

Consider the vectors A= (-…

02:05

Four vectors A,B,C,and D a…

06:40

Find the $x$ - and $y$ -co…

03:09

Compute with these vectors…

00:51

01:06

Write the vectors $A, \vec…

05:15

For the vectors $\vec{A}, …

03:02

Suppose $\vec{C}=\vec{A}+\…

this's Chapter one problem. 44. In this problem, we are looking for the X and Y components of the three vectors drawn in figure 1.2 for which you should have in your textbook. So what the figure gives us notice for each vector were given a magnitude so the length of the vector and were given an angle. So when we've got magnitude and angle or some kind of direction we convert to X and Y components using the equations on the board right now are ex component. Our subjects is able to Argos on data, and our white component are wise. People are signed data where our is the man into the vector and fada is the angle between the vector and the ex access measured counterclockwise from the X axis. So here, in all cases, we are given the magnitude of the vector directly. We could just read back off the diagram for the angle. We're going to have to do slightly more work because not all of these angles are given measured counterclockwise from the X axis. So let's start with Vector A. It's in our first quadrant. That's couldn't we Maybe these used to think about. Leave that a X is going to be put in our magnitude 12 meters, 12.0 meters, but I'll just write to 12 Oh and co. Sign of our angle now were given an angle of 37 degrees with the Y axis. The angle with the X axis, which is the one we want, is going to be 90 degrees minus that, because from extra wise 90 degrees. And let's actually draw that over here. So you got R X her? Why our aid? After and so in red. This whole angle is 90 degrees. We're given in blue this 37 degrees, so the one we want should be the whole thing. 90 minus 37. Or, in other words, we've got 53 degrees, and that will get you are a sad Becks. If you plug that into the calculator, you'll find this is 7.2 meters. And if you plug it into your house later and did not get that check, whether you're in degree mode or radiant mode from using that kind of calculator, that's a common way people get tripped up. All right, for a CE of why we've got our magnitude. We already did the work to find our angle. So we're just gonna right out the same thing 12 meters. But now we're going to sign a 53 degrees and again plug that into your calculator and you get 9.6 meters and we could do a quick check to see that these seem reasonable. First, both of these are less than 12 meters, which is good of after component. Could never be more than the vector magnitude. And if we look on the diagram, we see that the y component, it sort of sketching out in black here looks like it's going to be greater than the ex component sketched out here. And we find that is what we found numerically. So that's great. Alright, next factor. We're going to do a similar thing, Dr B, in your diagram here we've got our magnitude is 15 meters, so we can just plug that in for our ex component. For angle, we're given a 40 degree angle with the ex access. But remember, we want our angles fii measured counterclockwise of the X axis. And this thing is drawn clockwise from the X axis. So Basically, it's like we're moving in the negative direction so we can call this angle negative 40 degrees. Now it turns out for the Cosa and putting a positive or a negative on the angle won't make a difference. But it will make a difference when we do the sign and we can see that again. Well sketched this out here got R X and why access the be vector all drawn black was down here. If it had been positive for you degrees, it would be up here or blue is and you can see maybe the ex component. Either way is going to be this line and read same thing. But the y component. If they did, we're positive. 40. It would be going up. It would be positive status. Negative 40 is going down. It's going to be negative. In any case, for the ex component. We've got that all written out. Put it into your calculator and you're going to find 11.5 meters for your answer and for me. Why? Where youse Same magnitude, same angle, but now a sine of the angle. And so we expect from the diagram I spent to get something negative and we expect to get something smaller than 11.5 meters and indeed would get minus 9.6 meters. So that seems reasonable. That checks out all right on to the last one. Vector See So, Director, see, we have it drawn. Our angle is clockwise of the negative. X axis is what strong here. So put vector See in black our angle fade out here were given a 60 degrees. But what we really want to put an art to putting our equations is the angle measured from all the way over here. That's going to be 180 degrees all the way around to the negative X plus that 60 degrees or 240 degrees. So C X ex component of C. We know our angle is 240 degrees are magnitude is six meters. Read that directly off the diagram. So we're going to do six meters. Time's a co sign of 2 40 degrees. Pop that in the calculator and you get minus three meters exactly for the white component. This one. Hopefully you know the pattern by now same magnitude, same angle, but you put in a sign and you get that C. Why is six meters time sign of 240 degrees, and that's going to be minus 5.2 meters. So let's truck That makes sense. Both See X and see Why are both negative? Which makes sense, because there in that negative negative quadrant over there and see why is going to be larger than CX, which again makes sense. I didn't draw quite like that, but that 60 degree angle it's greater than 45 degrees. So this vector is more vertical than horizontal, so this all checks out.

View More Answers From This Book

Find Another Textbook

02:11

\cdots In one form of cataract surgery the person's natural lens, which…

02:36

$\bullet$ (a) A cylinder 0.150 $\mathrm{m}$ in diameter rotates in a lathe a…

08:40

$\bullet$$\bullet$ Two boxes are connected bya light string that passes …

03:28

. A water balloon slingshot launches its projectiles essentially from ground…

09:39

With a 1500 $\mathrm{M\Omega}$ resistor across its terminals, the terminal v…

07:03

$\cdot$ $\cdot$ $\cdot$ A 1.50 $\mathrm{kg}$ book is sliding along a rough h…

01:30

Plate tectonics. The earth's crust is broken up into a series of more-o…

01:18

Lightning strikes. During lightning strikes from a cloud to the ground, curr…

01:36

A wire 6.50 $\mathrm{m}$ long with diameter of 2.05 $\mathrm{mm}$ has a resi…

02:18

$\bullet$ In Figure $10.44,$ forces $\vec{A}, \vec{B}$ $\vec{C},$ and $\vec{…