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The three displacement vectors in B thf drawing have magnitudes of A = 5.00 m; B = 5.00 m, and € = 4.00 m. Find the re- sultant (magnitude and directional an...

Question

The three displacement vectors in B thf drawing have magnitudes of A = 5.00 m; B = 5.00 m, and € = 4.00 m. Find the re- sultant (magnitude and directional angle) of 60.09 20.08 the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative X axis: 47. mmh Multiple-Concept Example 9 re- a role in this Problem 46 views the concepts that play problem. Two forces are applied to a tree

The three displacement vectors in B thf drawing have magnitudes of A = 5.00 m; B = 5.00 m, and € = 4.00 m. Find the re- sultant (magnitude and directional angle) of 60.09 20.08 the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative X axis: 47. mmh Multiple-Concept Example 9 re- a role in this Problem 46 views the concepts that play problem. Two forces are applied to a tree



Answers

The three displacement vectors in the drawing have magnitudes of $A=5.00 \mathrm{m}, B=5.00 \mathrm{m},$ and $C=4.00 \mathrm{m} .$ Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative $x$ axis.

All right, Sweet will come back. So for this problem, we have three vectors. Well, docking my equipment clean and green Cream is lovely color. All right, sweet. And then we have three vectors. Your one Quinn's down the length of four meters. Quote electricity. Victor, See one points going up into the right here. Birmingham, England. 60 degrees court Vector B. That's a magnitude of five meters. Another one kinda points off that direction forming inning with 20 degrees magnitude of five meters and we caught vector A All right, so you want to find the magnitude and direction of the resultant vector there. To do that, we need to get out of the X and Y components of these three vectors right here. So it's kind of do that off to the side. First will be the X components. So the extra bones all right for really see doesn't have an extra point, only A and E. And to make this slightly it more sense water by defined up to be positive into the right to be positive. So the x component of a then it's a negative. You give five crusade 20 that be compliant. Let's go by five because it's a magnitude of five meters times the co sign 60 degrees that will give us native 2.2 meters from nowhere. Victor's coming. It's going. Teoh fears the origin is gonna point somewhere off to the left. Here, find the lightning. Born is no. Um, so you have five sign or 20 that will give us the height of this vector in your white component victory, plus the y component of Victor B. That's skilled by five times the sign of 60 minus four because the specter of literacy is all in the negative white direction, and that will give us positive two meters. So you know where vector is gonna look something like this? Something like that. It's going to have the X compliant with a magnitude of 2.2 meters and its height. Just gonna draw right over that right there. This two meters. All right, we want to find We'll call this victor. Are Art is a nice love letter. We're gonna find the magnitude end. The England are forms with the X axis. This single rate here call up data. So to find the magnitude, here's a vector. I We'll take the magnitude of it. That means we're gonna use Pythagorean theorem. It's like my favorite term. You use it all the time is so lovely. All right, you do that. Put that into your calculator and and this is one side book the square, one side, plus the square of the other side that will give you about three meters. Then we can use two engines to find the angle that it forms with the X axis. So you used tangent or write it off to the side. Your tangent of the angle. Fada succour to the opposite side over the adjacent aside. So gift engine to Athena sequel to the opposite side, which is two meters or the adjacent side register. Put two meters. We can take the university in Genoa. Besides, to do now, if us approximately 42.3 degrees and sort of their your final answers

We want to find the magnitude and direction for two vectors. First, vector A with components negative 30.0 m negative 50.0 m, and vector B with components 30.0 m 50.0 m. This question is testing our understanding of the relationship between vector components and magnitude direction, so we'll proceed as follows. First of all, we know that the magnitude of vector V is equal to a squared of the expectancy, Y square and the direction is equal to the arc tangent of the Y component of the X component B, Y O. Of the ex arc tangent, also known as the inverse tangent. Note that we add 180 degrees if the vectors in quadrant two or three, the first director A. The magnitude is negative 30 square foot section 50 square to 58.31 m. And the direction is 100 degrees, are tan Magnifico negative 30 equals 239.4 degrees because it is in vector or rather quadrant three. Next to be, the magnitude is 30 square plus 50 square square root, or 58.31 m. And direction is stated B is equal to our temperatures over 30 equals 2 to 9.4 degrees, and this is because it's in quadrant one.

So this question is asking us to find the, Find the magnitude and an angle of of of three vectors a. And also under under combinations. Mhm. So adding together and subtracting A B and C from each other. So, first of all, before we can answer any parts of the question, we need to work out what the vectors A B and C are are in component form. So since we're given the magnitude of AB&C is 50 m And the angle uh the angles are 30° 195° and 315° respectively. We can just work out a B&C. So 50. So we know that a 50 costs of 30 I had plus 50 sign of 30 jihad. So if we work this out we get that is equal to 43.3 m 43.3 m I had plus 25 jihad seven. And we can do the same for be so 50 costs of 195 I had. Is he the -48 .3 I had And mine is 12.9 Jihad. Okay Then proceed we can do the same. 50 cost of 315 of the 35.4 I have. And then for J had because it's -35 0.4 J. Hat Right? So now that we've worked at this, you can move on to part A. The party is asking us to find friday asked us to find the magnitude of A plus B plus C. So for a we first have to find out what a place people see is. Apis people see is equal to so adding together like components, so adding together the eye components from A B and C, adding together the J had components from A B and C. So we get the HSB for C is he was a 30.4 I has and then I don't have the Jayhawk opponents. We get -23 points three Jihad. That's a plus people. See them to find the magnitude of eight. To speak to see. We stood in the usual way taking the square root of the, of the some of the components squared. So it's gonna be 30.4 squared Plus -23.3 squared. This is equal to if we work this out, so this is equal to 38.3 years. Yeah, that's our answer for a 38 point through 38.3 m. Mhm. To prepare fee, if we find the angle B is to the anglo able to policy. So that's the theater is equal to tan inverse of the white component over the x component, that's minus 23.3 over 30 0.4. So if you work that out, we got to the angle of the back to april CPI C is equal to minus 37.5 measured from the X axis. But if we want to measure anti clockwise from the from the positive X axis We get this angle is equal to 300. Taking, subtracting that angle from 360 with at the Angle is equal to 322.5 degrees. That's your answer for our beat. If we move up to the top right corner parts for parents seat. Mhm Part she asks as far as she asks is about the factor A minus a minus B plus see So let's work it out then. So adding together the light components of A and C. And so adding together extra points of A and C. And I get together white components of A. And C. And subtracting the X. Components of B. From from the from A plus C. And then so yeah so we had together the eight the the X. Component of A. And C. And we subtract to beat the X. Component of the from that answer. Then we add together the X. X. And X. Or the Y. Component of A. N. C. And then subtract the white part of the from that answer to get what A plus A minus B plus C. Is equal to. So we do that. We find that's equal to 127. I had mine or plus 2.5 jihad to do. So we're doing that we get our answer. It was a minus B plus C. Identify the magnitude just the, you know, the usual magnitude formula A. For A. For the vector. So we just take the squares Of the x component squared, 127th squared plus the y component squared which is 2.5 square. If we work this out we get that a million people see is equal to the magnitude of is equal to 127 years zero rounded to one decimal place. That's your answer to see them for R. D. For us to find the angle. So the angles even a theater is you have to turn inverse of The white components. That's 2.5 Over the extra 100, you work that out. This is equal to 1.1°. And since both the X component of a minus people see and and the white components are positive is in the first quadrant. So this is the right answer. than for part E. We're asked to find vector D. Such that a such as satisfies a frisbee minus C plus D Is equal to zero. So then that's highlight our previous answers. Or 1.1 1.1° And 127 m. Yeah. Say if we scroll down, the party is asking us to find a electricity such to satisfy this equation. Mhm. So this is basically we can treat this like any algebra equation where a B. For a B where D. Is the variable that we want to solve such linear algebra equation. Just a normal linear equation. So if we multiply out the minus bracket for on the bracket C plus D. We can just bring sti over to the other side to find what D. Is equal to. So doing that was playing out and bring indeed to one side. We got the D. Is equal to A. Must be minus C. Then if we add together the director is A plus B and subtract, see so we add together the component, the like components of A plus B and subtract the light components of C. We get that the answer for D is 3.4 I had And plus 47.5. Okay. The class, It was 47.5 Jihad. And this is our answer for what it is then. So now we've done that. We can find out the magnitude and the direction of the Yeah, yeah, yeah. So let's work out the direction direction or the magnitude city the magnitude of D is equal to the square root Of -34 square. Thus 47 7.5 squirt work this out. We get that the answer for this part of the question is so we find out that the answer for this part is then Uh 56.4 m. Then for the central part uh In for part F by the angle mhm. So ash, he had an equal to tang inverse of 40 sets the white about 47.4 over mines 30.4. How? So if we work this out, we get to the angle of the equal to -57.4. But with this angle this act since the Y component of these is positive for the X component is negative. This must be in the second quadrant. So we take 57.4 away from 180 degrees. To get the anger is 126 122.6°. This is managed with from the positive sense of the real access anti clockwise center are answered for parts, The answer is 126.6°. for part there

Yeah. Here we are given three vectors. Yes. Mhm. Lead and see. Each has a magnitude of 50 m And he makes an angle of 30° with respect to X. X. is while B. Makes an angle of 1 95 degrees it accepts and C max and angle of 3 15 degrees it accepts is so Oh the diagram will be looking like. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Mhm. This is a tough be better And see at each with magnitude 50 m. So for the 1st 1st question whether we need to calculate the magnitude of Yeah plus B. Let's see that's so if we decompose the X. And Y components for every vector we'll get after equal to 15 cost 30 degrees. Yes plus 50 sign Yes. 30 please. I can't. Uh huh. Check it. Okay. And be the total vehicle to 50. It was 1 95 degrees ica flask 15 Sign 195° Jacob and serial equal to 15 cost 3 15 icap less 15 signed three system Jacob. Yes. And if we do a pleasant square pleasure. Yeah. Okay let's see equal to your fleet. Get common of 50 and we'll be getting of course 30 plus costs 1 95 plus because 30 15. Yes. Yeah. Mhm. Are you can yes 15 sign 30 left. Sign 1 95 plus sign three different that's fine. Uh After calculation will be getting 30 point three I can't minus yes 23.3 Jacob. The magnitude of this will be equal to. Mhm. What the world? Yes 30.3 squared last -23.3 square. That would be able to 38.3 meters. Yes. Yeah. Yeah. Yes yes yes. So so the answer for problem there will be Mhm. 38.3 m. As for B. We need to find the angle of uh oh this A plus B. Uh Air problems we will be a problem. So for that, wow. Yes handle yes. Yes tita equates to if we can store the trigonometry then cause will be equal to side by high partners. So 30.36. Right? That 8.3 Yeah That would be for two. Thank you. 37.5°. Mhm. Yeah. Mhm. For the bulls problem see we need to find the magnitude of like the yeah minus B plus C. Yeah that's this would be equal to yeah. Mhm. That's right. Yeah 50 times. So cost 30 minus Cost 195 plus cost 3 15. Yes plus 50. Yes. Sign 30 -195 Plus sign 3 15. I get my Jacob this will be on after calculations. This will be equal to 1 26.9 I get less. 2.5. You take care so the magnitude of this will be because Mhm. Okay. Oh the war 1 26.9 sq Plus 2.5 sq. Okay. Yes, that would be equal to yeah. Yeah. 1 26. 197. Similar to 1 27. Yeah. No, for the part of E we need to find the angle uh angle Yeah. The Evil Menace video surplus sector mix. Yes, that's called tita dash. That will be equal to because in myself, 1 26.95 by 1 26.97. That would be required to one point to respect. Yeah. Uh huh. No. Mhm. Sorry, this will be part of the it's christmas for the part E. We are given a certain conditions that the editor plus leader to minus c Vectra plus director Equal to zero. And by using this condition we have to find the magnitude of bigotry. So if we send director to the side then it will be able to Just me to -7. That would be equal to 50 times cost 30 plus costs 195 minus because 3 15 I kept to us. Yeah. 15. Sign 30 mhm Plus sign 1 95 minus sign today. 15 Jacob. Uh huh. Mm. This will be equal to box minus 40 one three I guess first 47.41 Jacob Yeah the magnitude will be equal to so uh Yeah 40.3 Will Square last 47.41 squared. That will be equal to 62 25 Mhm. Yes. Yes. Yeah. For the problem of f we need to find the angle that the venta Mexico X axis. Let's call it five. And that would be called do of course it was off -40.3, decided by 62 125. That will be equal to 1 30 point four degrees. Yeah.


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