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A person starts walking from home and walks: 3 miles East miles Southeast 4 miles South 2 miles Southwest 2 miles EastThis person has walked total ofPreview milesFi...

Question

A person starts walking from home and walks: 3 miles East miles Southeast 4 miles South 2 miles Southwest 2 miles EastThis person has walked total ofPreview milesFind the total displacement vector for this walk:PreviewIf this person walked straight home; theyd have to walk pninsPreview miles

A person starts walking from home and walks: 3 miles East miles Southeast 4 miles South 2 miles Southwest 2 miles East This person has walked total of Preview miles Find the total displacement vector for this walk: Preview If this person walked straight home; theyd have to walk pnins Preview miles



Answers

A student walks $100 \mathrm{~m}$ west and $50 \mathrm{~m}$ south. (a) To get back to the starting point, the student must walk in a general direction of (1) south of west, (2) north of east, (3) south of east, (4) north of west. (b) What displacement will bring the student back to the starting point?

To calculate the result of displacement off the person walking. We first calculate the individual displacements in terms of their I N J components. So for each part of the journey, we calculate this displacement in terms of the X and Y components. So for the first straight land, Todd, the displacement is simply 100. And that's in the Eid erection or the X direction. That's one d two. We can see you since U minus 300. I direction do three as both X and white components and has an angle so minus 150 and the co sign off 30 degrees. And that's gonna be I direction minus 160 sign or 30 degrees. And that gives us the J component. And if we simplify, that reaction will make that simpler. If we perform the trigonometry and this is minus one on that team, I direction minus 75 j direction. Finally, you do the same for the final straight man pot. Get minus 200 co sign 60 Devi's I comported Yes, 200 times sign 60 days for Jake Compartment and simple like this. We get minus 100. Yeah, I direction. Bless. 170 regeneration. Now we have all our streamlined parts resolved to the Iron Jake appointments so we can calculate the resultant just basement are and the results and displacement are It's simply the sum. Okay, took space minutes one. Let's do too best before. And if we add all the light components of the eyes on the jays, we get that far is minus 100. And that you? The eye direction minus 202. J direction. And that's meters so we can resolve this foot that we have the Senate's X and white component phone. We can get it in another phone, which is its magnitude and its direction with respect to the positive expenses. So the magnitude we know the displacement is the square root, but the X component that's the white component that's minus 150. The X component squared plus minus 202 squid, which the Y component above. We get magnitude of this basement. 240. Meet us now we need direction. Technology. We can see from all angles. Heat up and fight green tick. Okay, the angle pita, which the angle respected the positive xxx We can see that the angle Phi is up 10 off this white component over the X component 130 both negative, and so we can write them as positive, positive and forget. Fight to be 57 going to greet wherever we wish to find Etem Beato. He's 180 degrees. Thus five, and hence we get data to be 200 37 degrees. So now we have our in terms off its magnitude at its direction.

Here for the solution. As one equal 200 I, as we call to minus 300 Jacob as for equal to minus 1 50. Khowst 30 icap minus 1, 57 30 Jacob, which is equal to minus 1 29.9. I kept minus 75. Jacob, as for equal to minus 200 costs 60 I kept plus 260 Jacob, which is equal to minus 100. I kept plus 1 73.2 Jacob. So from here as well be equal. 200 ICAP minus 300. Jacob minus 1 29.9. I kept minus 75. Jacob minus 100. I kept plus 1 73.2. Jacob. And from here we get as equal to minus 1 29.9. I kept minus 201 point at Jacob. Bye. Being on the road and square, we get as equal to underwrote. Minus 1 to 9.9 whole sky plus minus 201 Pointed all square, which is equal to 2. 93.9. It had. This is the s Now for the Cheetah Cheetah called Lieutenant. Words minus 201.8 but minus 1 to 9.9. From here, we get here is equal to 1 57.23 degree below at success No. 57.23 plus 1 80. This is equal to 237.2 degrees from positive X axis, which is our final answer. So this is the solution. Step by step. Please go through this. Thank you.

In the given problem, the parts followed by market rate are given. So to draw these parts, you could have toe did you the directions north, south, East, west if you draw them here. This is not south in the east. And this So the part of the Margaret is as given doesn't fall. She's moving 0.500 miles west. It's like and grow like this and I will consider it to be 0.500 in the park is marked as from o toe a 0.500 miles. No. From here she turns not and move 0.200 mice. She turns north and moves like this. Suppose I do Destination B and this is 0.200 miles. Finally, she turns east and move 0.300 miles. She turns east and moves 0.300 Minds up to here. We mark it a C and it is 0.300 mice. This is the final destination off Marguerite. No, what is her total displaced man? So our total displacement will be represented by this arrow up to here and we have to find it. The displacement. So for this displacement, we have toe draw the components off this displacement, the complainers, maybe one of the component is this up to here along Negative accepts is and another company until, say this here along Also my access because in orderto show the components off a given rector we should draw the perpendicular from the tip off the vector. Do the access. So if you consider the displacement Toby are this will be It's like home owners and this would be yes, x component. So if we take this measure, man, clearly the component are X is coming to be equal toe or a minus. B C means it is 0.500 miles minus 0.300 mice means to save 0.0 miles. And it's so why come born in is exactly equal to a B which in magnitude waas equal toe 0.200 miles. So the next displacement are will be given with the help of Pythagoras Terram as our excess worthless our vice where means 0.200 square less 0.200 square my eyes means from C wise off 0.200 square miles which will become equal to 0.0 will come out off their square root. And inside it is too. Which is 0.200 into 1.4 one four My eyes or finally the lamp off this displace man becomes equal toe 0.41 14 to 0.20 point 28 meet nice. This is the lamp off the final displacement off, Margaret from no starting point. What is the lengthen direction? Yes, we have to find the direction also from vest. So I consider. If I consider this angle to be Tita then and Pita will be given by our wide by our ex. So it will be equal to 0.0 Divided by 0.0 both in miles. So dancer here will be one. So Tita will be 45 degree. So I can say the direction is north vest. The direction is north. This

This exercise. We have a trapper Woakes, a distance of five kilometers with ah direction off 40 degrees to the north of the X axis. And what we have to do is to calculate the components of the displacement vector off the trapper. So let's do it. The displacement vector is this blue vector here, Um, with a magnitude of five kilometers, I'm gonna call the displacement vector A. So A is equal to a axe, which is the X components times the unit vector in the X direction I plus a why j which is the unit vector in the white? Yeah, direction. So a X is equal to the magnitude of a times the co sign of 40. So this is equal to the magnitude of a is five kilometers times the call sign of 40 which is equal to 0.766 and a X is equal to 3.83. A y is equal to the magnitude of a times the sign of 40. So a why is able to five loners times 0.6 for three, which is equal to three points 20 work. So the total factor is equal to 3.83 i plus zero after three points. 21 j kilometers. What? Okay, Then we have to calculate how how many more kilometers this trapper would have to walk if she chose to walk in a straight line along acts direction and then in a straight line along the wide rash. In that case, the total dis and she traveled would be a total distance would be the X component a X plus the y component A Why this is 3.8 e three plus 3.21. So this is equal to 7.4 This is the total distance you would have to travel. And since when she walks in a straight line, she travels only five kilometers and the difference in the distance don't A D is equal to two point 2.4 kilometers. So she would have to vote 2.4 cloners more then she does. Ah, and finally we have to say what is her displacement of actor? So notice that either way Ah, this matter If she she walks straight to the finishing point or if she Woakes first, uh, along the X axis and then along the y axis, uh, along the y direction? Sure. Ah, her displacement vector will be the same because of this basement. Vector is the vector that connects the starting point in the finishing point, regardless of the trajectory. So her displacement vector would still be the defector with magnitude of five kilometers with an angle of 40 degrees with the X axis, and for the reason her despite displacement vector would still be 3.83 i plus 3.21 j kilometers.


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