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Rent ConsantsAspelunket anvuying a cavo.51a follows a Daeseot 160 m slraigh wust ten 210 t in a declon 45 e45 olsoulnand tran 280 = east ol north Aller & Iourt...

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Rent ConsantsAspelunket anvuying a cavo.51a follows a Daeseot 160 m slraigh wust ten 210 t in a declon 45 e45 olsoulnand tran 280 = east ol north Aller & Iourth unneasued displacemant ea linas harsall back were she HendPant pUso = scala Cara coretmino Ihe magniluca Ehe "ourth displacement Expres> YouI ans tel MielertAzdSucRenutel Amatun

Rent Consants Aspelunket anvuying a cavo.51a follows a Daeseot 160 m slraigh wust ten 210 t in a declon 45 e45 olsoulnand tran 280 = east ol north Aller & Iourth unneasued displacemant ea linas harsall back were she Hend Pant p Uso = scala Cara coretmino Ihe magniluca Ehe "ourth displacement Expres> YouI ans tel Mielert Azd Suc Renutel Amatun



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Peggy drives from Cornwall to Atkins Glen in 45 min. Cornwall is $73.6 \mathrm{km}$ from Illium in a direction $25^{\circ}$ west of south. Atkins Glen is $27.2 \mathrm{km}$ from Illium in a direction $15^{\circ}$ south of west. Using Illium as your origin, (a) draw the initial and final position vectors, (b) find the displacement during the trip, and (c) find Peggy's ayerage yelocity for the trip.

Problem we are given exploring travels 30 m due east. So this is 30 m divest and then 22 2 m in the south of east. So this is 22 m and then travels 1 40 m in the direction of north. We have to find the displacements would be well with the displacement. Now we will find this distance. This distance will be acquitted two. 20 route to into cost 45. So we know that 20 route into cost 45 years one way road to so This is equal to 20 m and this distance is also equal to 20 m and this is also equal to 20 m. So now this distance will be equal to 1 20 m, right, And this distance will be equal to 30 plus 20. That means 15 m. So the displacement will be equal to 50 square plus one 20 square. So this is Yeah, I watch come Good cooker today. Hi,

This time. We'll be looking at a problem. 11 from the after two of physics. Fifth book, The question states a woman walks 250 m in the direction. 35 is to look And then 170 m from the east. Using graphical methods. Find her final displacement from the starting point and then compare her magnitude of her displacement with the distance booked. So just as a graphical representation of what's happening here is asking the question that are women walking 250 m uh in this direction here 35 degrees um east of north. So again we started we started the north and we're going 35 degrees east of north, 150 m. And then 170 m directly east. And we want to know ah displacement which is marked by this green dotted line with question mark. This is how far away she location. So if we work out the total, we need to split all of our vectors up into vertical and horizontal components. So our total vertical displacement Um is just 250 multiplied by cause 35 using um force Dakota. I will be using in this case. So we get 250 most applied by cause 35 is equal to this vertical thing. Um And uh as this line is only in the east direction it has no vertical components. So we just get that B 205 m. And then the horizontal displacement we do now we use so and we get 250 sign 35 degrees um to get this here And then of course we're adding onto that 170 m. And so we get in terms of 313 m, the final displacement start will just be using Pythagoras theorem and we get two of the square root of two oh five squared plus 3 +13 squared. And that gives us 344 m 374 m. Um And then the question asked, part B to compare the magnitude of the final displacement with the distance walked. The distance that she walked is just going to be 250 plus 1 70 which 120 we're gonna subtract 370 for that, which is a displacement. And we get 46

A bird watcher goes .5 km to the east, so start here we go, .5 km to the east, And then .75 km south 75, and then 2.15 kilometers in a direction 35 degrees north of west. So let's parse that for a second. North of west. Well, west is this way north of west, would be that way. So north of west is going to be sort of at the direction like that And that angle right there is going to be 35°. So starting from where we left off, we're gonna go uh huh. Far ish, At an angle of 35°, we're gonna go to 15 km. We need to find the magnitude and direction of their displacement and average velocity. The good thing about displacement is, it only considers the beginning and ending. So all we are really worried about is from here to here. So, uh the way I would approach this, since we've got a number of different vectors, let's consider each vectors, X and Y values the first factor Goes .5 to the east. Well that's only in the X direction, so that's .5 directions, .5 km. Uh And in the Y direction it doesn't go up or down at all, so it would be zero In the 2nd 1, This .75 here, it goes straight down, so it's not going left to right, but it is going vertically downwards. So that's negative .75 km And then there's 2.15 km at 35°. I'm gonna need to use some trig for that would set up a nice little triangle like this and recognize that this is 2.15. And here's my angle. So I'll use co sign to find the X component. I'll use sign to find the Y component, Leave the details of that to you. But it turns out that in the X direction it's negative 1.76 kilometers and in the Y direction it's 1.23 kilometers. So when it all comes together, what I really am concerned with is the grand total of all the exes and all the wise Turns out that the grand total of all the exes is negative 1.26 km and the grand total of all the Y values is .48 km. So that gives me a new triangle which goes 1.26 km in this direction and .48 km in that direction. So this is all I need to worry about at this point, I'm going to redraw that in green down here, 126 and .48. And what I really need to know is this answer right here. So we've got a right triangle, there's a pythagorean triangle. So do 0.48 squared plus 1.26 squared is going to give him a hot pot news. So my high pot news is Going to be, turns out to be 1.35 km. And I also need to figure out this direction right here. So you need to use trig. The tangent of an angle Is equal to the opposite over the hypotenuse. In this case the opposite is the Y value. So that's going to be .48 Over 1.26, sorry, opposite over adjacent. So .48 over 1.26. That's the tangent of the angle. And I need to find the angle. So I need to do inverse tangent of the angle itself is to go to the inverse tangent of .48 over 1.26. So Inverse Tangent of 4 8 divided by 1-6, gives me 20 0.8 degrees up in this direction, which again is going to be north of west. And what we need to find out is the displacement, which effectively I have just done because we know the total length or the total uh displacement from where they started to where they are now. So they're going to be 1.35 km away from where they started at an angle of 20 degrees 20.8 degrees north of west. So there's our displacement And the velocity is simply displacement divided by time. So uh velocity displacement divided by time. Other displacement was 1.35 km and it took time of 2.5 hours. So 1.35 divided by 25 hours is .54 km/h, and they were in the same direction. So that same direction applies .54 km/h, at 20.8° North of Quest. There is a displacement. Here's our velocity.

In this question. We've got a shopper pushing a cart down a Siris of aisles, making two turns before the motion is complete and were asked to find what the shoppers A total displacement is, Um, and there is a no in the question that there could be more than one correct answer. And in fact, there's actually four correct answers. Four possibilities. Because if you think about it each time the shopper turns 90 degrees, there's two directions in which they can turn. So, for example, if you take a look at the first scenario here, the shopper walks 40 meters south, and then they can either turn 90 degrees to and go to the right or turn 90 degrees and go to the left. And then, of course, for the second turn, they can turn up or down. So combining those combinations for the turns, we get four different scenarios here. Okay, on What we need to find is the result in factor for each of these scenarios. So remember that the resultant vector will points from the starting point to the finishing point. So I'll just draw these on so you can see what we're trying to find here in all of these cases. And the good thing about these four scenarios is there is a little bit of overlap, right? So you can kind of see that the magnitude in A and B of for the displacement will be the same, and the manner to between C and D will be the same. And there's also a little bit of, um, a little bit of overlap with the directions as well, which we can discuss. So let's start by finding the magnitude. So we'll start with scenario and be and we'll find the magnitude of these two vectors, which, as already mentioned, should be the same now, in terms of the X direction, it's clear that the components of this result in factor is just the 15. That's the only vector that contributes to the X component here. And then the y component would be 40 minus 20. Okay, So, in order to calculate the magnitude of the displacement here, um, so this is for A and B. The magnitude will be the square roots of 15 squared, which is the X component plus 20 squared, which is the y component. Now, of course, this vector B points in the opposite direction for the X direction. But we don't need to worry about that in terms of the magnitude. So when we solve this on the calculator, we get that the displacement here is 25 everything is measured in meters. So the displacement, the magnitude of the displacement is 25 meters. Okay. And so what about the directions here? So in the diagram, these two angles here have to be the same gray. This is basically A and B are basically just a flipped a version of one another. If we flip along the 40 meter line, right, hopefully kind of do a mirror flip along the 40 degree line. We can translate A and two B and B into a. So the two angles that I marked in red here are the same. The only difference is you know, is it directed east or west? So we'll take into account that after we calculate this angle. So let's calculate the angle here. In order to do that, we will use tan okay, and we're using opposite over. Adjacent right, So opposite to this angle is 15 and adjacent to this angle is 20. And so when we take the tan inverse of that and plug it into the calculator, we look ants 36 degrees. So this is where the difference between the two comes in. What is it? 36 degrees with respect to write? Well, it's 36 degrees with respect to the South direction, and we swing either east or West. So for scenario A, the angle will be 36 degrees east of south. Another way to say that is that it is 54 degrees south of east. We can always just flip it around and do 90 minus, um, to get the other way of stating it. So basically, what we're saying in that case is that you know, we're measuring the angle with respect to east, and we had to swing, you know, 54 degrees down to get um, to get the angle. With respect to east and then for Scenario B, the angle can be stated as 36 degrees west of south, or it can also be stated as 36 0 sorry, not 36 but 54 degrees south of west. So the final answers here our displacement for a will be 25 to 25 meters, 54 degrees south of east. And for scenario B, we've got 25 meters, 54 degrees south of west. Okay, so those of our 1st 2 options and now we have to deal with C and D. So again they have the same magnitude, and angles actually are the same. They're just measured with with respect to different directions on the compass. So let's start with the magnitude. Okay? So the Y component of the displacement here will be 40 plus 20 this time, So that would be 60. Sorry, in the X component here is the 15 because that's the only rector that points in X direction. And so we plugged that into the calculator. We could see the magnitude here would be 61.8 meters. Okay. And we'll do the same thing to get our angle. So this time we're kind of looking at, you know, this big triangle. We're looking at the triangle that the displacement and the displacement in the why and the dissuasion in the X makes, and we're trying to find this angle here. Right? So the opposite side is 15 meters the adjacent side here is 60 meters, and so the angle is tan and verse of 15/60. Putting that in the calculator, we gets that the angle is 14 degrees. Okay, And again, we have just a slight difference in how that that angle is measured with respect to north, South, east and west. So for scenario. See, here it's 14 degrees, 14 degrees east of south and for Angle D here it's 14 degrees west of south, Uh, and we can also switch that around to measure it with respects to east and west instead of with respect to South. So if we want Teoh have a look at this angle instead, then we can just do 90 minus data. Okay, so all right, that outs. So we can you can see all of the different options ways of stating at here. So angle see is 14 degrees east of south yes, or 76 degrees south of east. And then, for Scenario D, we've got either 14 degrees west of south or another way of writing that is 76 degrees south of west. Okay, so in summary, displacement see is 60 1.8 meters 76 degrees south of East and Displacement D is 61.8 meters, 76 degrees south of west. So these four options here are the final answers. These are all of our options, all of our options for a displacement.


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