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Determine the resultant of the vectors with the given magnitudes and directions_ Positive angles are measured counterclockwise from the positive X-axis and negative...

Question

Determine the resultant of the vectors with the given magnitudes and directions_ Positive angles are measured counterclockwise from the positive X-axis and negative angles are measured clockwise from the positive X-axis_A: 557, 160.0" B: 1236,225.00The magnitude of the resultant is (Round to one decimal place as needed:)The direction of the resultant is (Type your answer in degrees between 0 and 360". Round to one decimal place as needed: )

Determine the resultant of the vectors with the given magnitudes and directions_ Positive angles are measured counterclockwise from the positive X-axis and negative angles are measured clockwise from the positive X-axis_ A: 557, 160.0" B: 1236,225.00 The magnitude of the resultant is (Round to one decimal place as needed:) The direction of the resultant is (Type your answer in degrees between 0 and 360". Round to one decimal place as needed: )



Answers

vectors $\mathbf{A}$ and $\mathbf{B}$ are at right angles. Find the magnitude and direction (the angle from vector $\mathbf{A}$ ) of the resultant. $$\begin{aligned} &A=1734\\ &B=3297 \end{aligned}$$

So to find the magnitude of the magnitude of resultant vector, we take the two vector magnitudes we square them. We some them, and then we take the square root. So in this case well, and then after that, we want to find the angle between them. So in order to do that, since it's from the vector A. We take the arc tangent or the inverse tangent, uh the overhead. So we know in this problem that a. Is equal to 592 And B is equal to 95. But making sure that we're in degrees mode, we see their magnitude is 623. Um and depending on where you're around hold this go 3 um Significant figures. So 623. And then our angle measure is going to be 18.2°.. And that will give us our final answers.

So it's important for us to remember the formulas for determining magnitude and determining the uh reference angle and this is of the resultant vector. So we know in this case that we have, I am the magnitude is equal to the square root of a squared plus B squared. And then we know that the state of measurement, the angle measurement that we're looking for is equal to the square root of a squared plus B squared. So with all this in mind we can plug in our values of A. And B. And this will be calculated for us. But it's important that we see the formula and know how to implement them. So in this case are a is given to be 3.086 and r. B is given as 7.143. So we have four significant figures, which means our final answer will be 7.781 and 66.63°

So we're gonna be given vectors A and B. And we know that they're at right angles. That makes things simpler and we want to find the magnitude and the direction um from the vector A. Of the resultant. So uh we want to take the square root of a squared. That's B squared. In this case we know that A equals 14.7. Yeah. Deep equals making point here. So our magnitude M is going to be equal to 24.2. And then our data, yeah, we know is equal to the inverse tangent or the inverse tangent. Okay. Of E over A. And or we can use our tangent. So at the time are tangent of the over. Hey, so we calculate that we end up getting is 52.56°- 52.6°.. And that's with a.

Berate walking, docked. So this problem you service goes that hopefully you've been understanding and developing over this over it. These videos over your time during physics and math. All right, so in this problem, you have three. Vector is the 1st 1 helical vector thing starts at the origin groups or something like that from in England. 35 degrees with the X axis. It has the manager of 145 units. Um, firstly, the units off, they're all right. Second, victory forms in England. 65 degrees with the critical with a vertical line. Great. Was north the third vector starting from that point. First inning glove, 15 degrees with the vertical. All right, so in this problem, it here we want to solve for the magnitude of this is Victor a right here, Victor, be Victor. See, you want to solve for the the magnitudes of Victor being Victor. See? So, um oh, please. He was triangle right here. Kind of buried in a lot of lines and markings, but we're gonna do a lot of things with this triangle right here. It's a pretty, pretty special triangle, I guess. All right, So we've got, um, your first. We need to find each of these English right here. This one, this one and this one. So we know that, um, this single rate here, just this one part of the angle, it's going to be 1/4 15 degrees because this single right here's 15 degrees and their along parallel plant, uh, lines with an intersecting line so the inside angles are gonna be equal to each other. So this right here, this little part of the gang was 15 degrees. Uh, this part right here, we confined by doing 90 minutes 35 which is 55. Which means that that fall angle, they're merely drawing trying over here with her measurements. Who's drive the train going? I'm gonna draw on the board too. Well, it'll be a challenge, but I have faith that it'll work. Marriage. So this thing right here was 55 plus 15. That's gonna be 70 degrees. All right, this single rich here, we can find that by taking over here, we have the straight lines about 180 degrees minus, um, 65 degrees when this thing we're looking for. But it's this angle groups, ministers angle right in here, which we can find that angle fixing that Lansing. That's when you degrees 19 my just 35 rather 180 minus 90 minus 35. That gives us 55 degrees for this Ingrid here. If we do 180 minus 65 minus 55 that gives us 60 degrees. Then once again, we have another triangle ridge right here, which has a total of 180 degrees inside of it. So if we do a 180 minus 60 minus 70 we will find that this single ridges went to be equal to 50 degrees. All right, And we have this magnitude right here, 1 45 units. So using the lob signs, we confined, the magnitude could be in C Whoa. It was a strange murky right there. In case you were running that was supposed to be in a all right, it's a magnitude of eight is 145 spending the managers of E and C. We can use a lot of science than that is we have a side, they said right here over the sign of its angle, which is the angle opposite of that side. So this I right here, missing right here. It's gonna be a court to the that same idea aside, over an angle anywhere else on our triangle. It's a pretty nifty law. If you didn't know it, now you do. We'll find be first we could find. See? First, it doesn't really make much of a difference. Um, miss choosing it to choose it. So we have to be in the 70 degree angle causes the That's the side angle combination that are opposite each other, promoted by both sides by sign of 70 implied that end your calculator will find that be is equal to when ingen 77.87 units. You can do the same thing for side. See, So I know the angle that's you're looking anything was 60 degrees right here and again, much playing both sides by sign of 60. Then plugging in inter calculator will find that C is equal to 163.92 units. All right, and there should circle those right for blocks around it. There are your answers


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