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EXERCISEHINTS: GETTING STARTED TM STUCKI Graphically determine the magnitude and direction of the displacement if _ man walks 50.0 km 458 north of east, and then wa...

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EXERCISEHINTS: GETTING STARTED TM STUCKI Graphically determine the magnitude and direction of the displacement if _ man walks 50.0 km 458 north of east, and then walks due east 25.0 km_magnitudekmdirectionnorth of eastEnter number Need Help? ReedllTkla IaIViewing Saved Work Revert to Last ResponseSubmit Answer

EXERCISE HINTS: GETTING STARTED TM STUCKI Graphically determine the magnitude and direction of the displacement if _ man walks 50.0 km 458 north of east, and then walks due east 25.0 km_ magnitude km direction north of east Enter number Need Help? Reedll Tkla IaI Viewing Saved Work Revert to Last Response Submit Answer



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A pedestrian moves 6.00 $\mathrm{km}$ east and then 13.0 $\mathrm{km}$ north. Find the magnitude and direction of the resultant displacement vector using the graphical method.

So let's start this off by drawing a little compass here. Just so you know where directions are. This is north, so east at west. All right, so we're walking west. She's going to be this way. And this is 220 meters and then we go north. Not quite as far, only 150 years. So we want to know what is the magnitude and direction of our displacement vector. So we started here, We end here. So we want to know what this line here is. And if we look at this, we can see that this is a right angle. So we can just use Pythagorean theorem to answer this question. So we're going to need the square room of 150 square, plus 220 squared, and the answer to that is gonna give us 266 point three meters. But then we also want to know the direction. So we probably I need an angle here so we can find this angle right here. We can do that using our tangent because we know that tangent of that angle that we're looking at their data equals R opposite over adjacent. So it's gonna be 100 and 50 over our t 20. So what we can do to get that angle there is due are inverse tangent, but you do guy. And so that gives us 34.3 degrees. But if we look at this and we put this on a compass just like we have over here, So why don't we take this and do 90 minus R 34.3 and so that gives us 55.7 degrees. And that's gonna be 55.7 degrees. That is this one. What? Here? So we can say 55.7 degrees west of north.

This exercise Supposed that you're traveling to the West 18 meters and then you stop and traveled to the north 25 meters. And in the first part of the question, we want to calculate how far you are from the starting point. So basically, I'm gonna what I'm gonna do, it's just set up according system here, where the y direction it's pointing upwards. That's the north, and the X direction is pointing to the east. So suppose that you first travel along the X direction, but ah, to the to the east for 18 meters. And then you traveled to the north for 25 meters and we want to know what is the distance from the starting point. Notice that these vector green is win Vic. Director, here is the sum of the vector that I'm gonna call A, which is the first leg of Virginia, which is 18 meters to the to the east. So it's minus 18 in the corner system that I chose times I is the unit vector in the X direction, pointing to the east meters, and we have to some A plus. B B is the blue factor, the one ah the vector for when you were traveling north. So this is 25 times JJ's the in effect er in the wider action commuters and we want to calculate the the displacement, the total distance and the total distance is just the It's the magnitude of the some of the two vectors. So this is the square root of 25 squared plus 18 square and this is 30.8 meters. This is the distance from the starting point. Then we have to calculate, but the displacement vector and the displacement vector d is just a plus B. So this is minus 18 I plus 25 j meters. This is equal to the displacement vector d. All I did was to some the components off, the better a m better be. And finally we have to calculate what is the direction of the displacement. And for that, I'm gonna calculate this angle right here this angle Phi Ah, this is gonna determine the direction of the displacement, but noticed that this angle phi is equal to the angle theater right here that I have just drawn. So if I it's able to actually for five plus data, is equal to 100 in 80 degrees. So what I'm gonna do is that I'm gonna find data. And then with that, I can find the angle. Phi so noticed that here the tensions off data is equal to 25 divided by 18. So the tensions off theatre is 25 divided by 18. So Fada is the ark tensions off 25 divided by 18 which is equal to 54.25 degrees. So the angle phi is 180 degrees minus 54.25 which is the same as 125.50 point 75. The Greeks. So this is the angle that the displacement vector makes with the X axis.

It's exercise. We have a professor that drives 3.25 kilometers north. Then he drives for 0.75 kilometers west and won't wait five. Killing herself and Argo is to calculate what is the final total displacement off the professor, The net displacement and the direction the way she drove s so basically what I'm gonna do is to consider each leg of his journey as one vector. So I'm setting gonna set up a cordon system such that the Y axis points to the north and the accesses point points to the the east such that the, uh, trajectory of the professor is compose off three point 25 kilometers north. It's this vector that points in the Y direction, then four point, and I'm gonna, uh, write it in the origin. So we have the vector of 4.75 kilometers to the west and finally the vector of 1.5 kilometers to the south. So the first vector I'm gonna call it the one. It's 3.25 j kilometers de to is equal to minus 4.75 I kilometers. Indeed, three is equal to minus 1.5 Jake lovers in the total displacement is equal to the sum of these three legs of the journey. So the warm was the 2003. So we get three points 25 miles, 1.5 j minus four points. Have any five I cologne letters. And just to write it in a more usual form, this is able to minus four point 75. I close 1.75 j kilometers. And with this information working right, you can find the magnitude of the displacement that's the square root of DX swear. So it's 41 75 square was de y square. So it's 1.75 spared. So d is equal to 5.0, six kilometers. And we also want to find the direction of this vector notice that the better D has a negative X uh, a component and a positive white important. So it's pointing in the second quadrant, and we want to find the angle that it makes with the horizontal. So we want to find this angle here. Fada, In order to find data, I'm actually gonna find this angle phi here and use that data plus five. It equal to 180 degrees. I noticed that later the attention off there will be able to de Why the momentarily Why divided by the manager of the X. So we get that 10 Geant off theatre is the magnitude of the wider. But it was elected D X so fine is equal to the ark tensions of the magnitude of the Y, which is 1.75 to write about the magnitude of D X, which is 4.75 and this is equal to 20.2 degrees. So Fada is equal to 180 minus two any point to which is 158.8 degrees. And this is the direction, uh then have to draw the diagram and show that ah ah, the diagram agrees qualitatively with the result we found so basically again, I'm setting up, uh, corn and system here and initially, the professor drives three point 25 kilometers north. So this is people in kilometers. Then he drives four 0.75 kilometers west and finally he dries 1.5. So So this is about 25 kilometers, please. Daughter displacement is the vector that connects the origin with the final point, which is this vector here. Notice that it still points in the third quadrant as we wanted to. Okay, and I noticed that it is necessarily bigger. It's in magnitude. It's greater than magnitude, then 4.75 kilometers. Eso It's consistent with the fact that the displacement, the magnitude of this waste minutes 0.5 point off six kilometers and this concludes our exorcists.

So the professor has moved people into five kilometers, not and then two point two kilometers west and then one point five kilometers south. Not that they're roughly to scale a specially choosen right were to be east upward. Toby, not on will say right eastward, which is right where? Direction Exact taxes on a Ford since y axis as usual. So the net displacement would be this after? No. If you say the first displacement was s one bar, second displacement is too bad on third displacement, a street bar. Then we can see that s one bar would be three point two five Jacob because it's three point two five kilometers long and is in the positive direction, which is the same as upwards. Now, the second, better as two is in the westward direction, which is negative X direction. Hence esto bar would be minus two point toe cap. Now rest. Rebar is downwards, which is negative y direction, and hence would be minus one point five Jacob. Now, to find the total result and displacement, we simply add them. It's one less esto lets us three. We can call this as far the total displacement if the ideas. Three. We can see that there is only one component which would give you my list. Two point. Oh, my cab. And then there are two J confidence, which would give you three point two five minus one point five Jacob, which would be minus two point. Oh, that's one point two info chick. Now, if you look at the diagram, you can see that this corresponds pretty properly bitter numbers. We know that the ex company two supposed to be negative on about toe toe and the white component is supposed to be positive. And about one point seven five under y component is slightly smaller. Then our ex confident in the dagger just fine. Now the magnitude ofthe this vector would be square root off the sum of the squares of the components, which would be to point to square. Let's one point seven five square. It's turned out to be two point eight one loungers. Now, if you try to find the angle, it would be in worse off white component by ex confident. It would be one point seven five bye minus tow to, of course, if he used less two point Oh, here we get thirty eight point five, please. But this angle would be the angle it would make with the negative X axis. The angle it would make with the positive X axis would simply be one eighty degrees minus. Had it on five, which is one forty one one five degrees, which is it seems reasonable because this angle is obtuse and seems to be about one. Forty one seems to be the proper one number.


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