what-are-the-direction-and-magnitude-of-your-total-displacement-if-you-have-traveled-due-west-with-a

Question

What are the direction and magnitude of your total displacement if you have traveled due west with a speed of 23 $\mathrm{m} / \mathrm{s}$ for 175 $\mathrm{s}$ ,
then due south at 12 $\mathrm{m} / \mathrm{s}$ for 285 $\mathrm{s}$ ?

Andy Chen · Accepted Answer

We&#x27;re traveling to west at a speed of 23 meters per second for 125 175 seconds and then due south at 12 meters per second for 285 seconds. Here I&#x27;ve notated the two directions that were movie with red and green respectively. And first let&#x27;s go ahead and try and find how far removed in the ex direction. And then how far removed in the wind direction for the X direction, removing at a speed of 23 meters per second for 175 seconds. This gives us a displacement of 4025 meters. Notice this is in the negative X direction because the speed here should be negative. So we have negative 40,000 and 25 meters now for the widest placement. We have a movement with a speed of negative 12 meters per second because we&#x27;re moving in the negative direction for 285 seconds. This gives us a why displacement of negative 3420 meters and now we can use these two accent. Why components to find the displacement vector, its magnitude and its direction here. We already have a right triangle. So all we need to do is find the punters here. The hype oddness is equal to the square root of X squared plus y square. Where have you playing in the numbers? You&#x27;re just d&#x27;oh negative 4025 meters squared, plus negative 3420 meters square. That gives us about 5282 meters, which would be the magnitude of the displacement vector to find the angle angle we&#x27;re after is this angle which will notice data they were called Data can be solved by using the interest engine function of why over hacks. Here we have tangent of negative 34 to 0 meters over negative for 0 to 5 meters and that will give us an angle of 40 degrees. But notice 40 degrees is pointing in this direction. So we need to go ahead and add 180 degrees to Orion. Uh, 220 degrees

Whitney Massock · Answer

So let&#x27;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&#x27;re walking west. She&#x27;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&#x27;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&#x27;re looking at their data equals R opposite over adjacent. So it&#x27;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&#x27;t we take this and do 90 minus R 34.3 and so that gives us 55.7 degrees. And that&#x27;s gonna be 55.7 degrees. That is this one. What? Here? So we can say 55.7 degrees west of north.

Guilherme Barros · Answer

this exercise Supposed that you&#x27;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&#x27;m gonna what I&#x27;m gonna do, it&#x27;s just set up according system here, where the y direction it&#x27;s pointing upwards. That&#x27;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&#x27;m gonna call A, which is the first leg of Virginia, which is 18 meters to the to the east. So it&#x27;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&#x27;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&#x27;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&#x27;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&#x27;s able to actually for five plus data, is equal to 100 in 80 degrees. So what I&#x27;m gonna do is that I&#x27;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.

Mayukh Banik · Answer

we&#x27;re moving 30 to the south and 30 to the east. So this is the resident victors, which is 30 square past 30 square square root. It was 30 who do to southeast also doing it. Victory, victory. Really? It is 30 square plus 30 square plus two times 30 times 30 course signed. The angle between the line D swears off that comes out to be 32 this is the as you break solution.

Mayukh Banik · Answer

de with B squared off submission its eyes square Thus summation Why I squared equals 7.21 m and theta equals r tangent off submission Y i over summation x i it was 56.3.

Surendra Kumar · Answer

in this case and it is told that the particle undergoes Many displacements. That his first is 35 m. This is given to a 30 35 m in south, Then it goes to 8.2 m in northeast and finally it goes to 15 m west. So I&#x27;m going to draw this diagram for this confusion so that this is the particle. And first of all it goes to This is 35 m in south now from year ago, 8.2 m Northeast. And from here it goes to the 15 m. So this is a 15 metre invest, This is 8.2 m in northeast and this is 3.5 m in south. Now we have to find the final displaced resultant displacement. So this is our initial position and this is our final position. So the resultant displacement is given by this. So this is the result in displacement that is lead, this is our Now we have been ordered, this angle is 45°. Now I&#x27;m going to so left disease are Y. And this is optics. So we can say that we have to find the value of Arba and directs and let this is, this is the Y component and this is X. Component. So first of all we can say that why is given by from Bagram we can say that wise 8.2 off signed 45° from here, we get the value of why and this is five point 798 m. So we can say that this is the value of Y and we have to find our way. So are Y is equal to? So Arwa is given by, that is why -3.5. So this is five 798 -3.5. So this bill comes out to be two point 2982 m. This is the value of our wife. Similarly, we can find the Rx. Sorry, first of all we have to find the X. So we can say that That X is given by 8.2. of course 45 degree from here. We get the value of X. And this is 5.79 eight m. This is the value of X here but we have to find this value. So we have to subtract 15 -1. So we can say that our X is given by 15 -1. So this will come out to be nine point 2017 m. So this is the Rx value. So we can say that resulted displacement is given by that is our is going to under root of our X square plus ry square Put the value of Rx and Ry so this is 9.2017 sq plus disease 2.29 Here to Holy Square. After solving this, we get the displacement and that is 9.48 m. So this is the resultant displacement. We can also find the angle. So from late. This is the angle here with the original lettuces data. So this is also, we can say that this will also equals two. Are why we can say that identity is beyond by So 20 to is written as ry upon Rx. So are we? We had calculated that 9.2017 upon this is 2.2 982. From here we get the value of Tito and I see that is 14° and this is from north off West. So we can say that. Our answer for this question is that is resultant displacement is given by nine points 48 m and this is it 14 degree of north of west. So this is the answer of our given fusion. Thank you.

Problem

Predict/Calculate Moving the Knight Two of the al…

Problem 39 Medium Difficulty

What are the direction and magnitude of your total displacement if you have traveled due west with a speed of 23 $\mathrm{m} / \mathrm{s}$ for 175 $\mathrm{s}$ ,
then due south at 12 $\mathrm{m} / \mathrm{s}$ for 285 $\mathrm{s}$ ?

Answer

$\vec{s}$ has a magnitude of $[5281.7 \mathrm{m}]$ and makes an angle of $\left[220.35^{\circ}\right]$ with positive $x$ -axis.

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$\vec{s}$ has a magnitude of $[5281.7 \mathrm{m}]$ and makes an angle of $\left[220.35^{\circ}\right]$ with positive $x$ -axis.

Physics

Elyse G.

Andy C.

Liev B.

Jared E.

Math Review - Intro

Algebra - Example 1

James S. WalkerPhysics

Elyse G.

Andy C.

Liev B.

Jared E.

James S. Walker

Physics