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A displacement vector D is given as 40.0 m at an angle of 60.0 degrees EAST of NORTH: The Dx component and the component of the vector are...

Question

A displacement vector D is given as 40.0 m at an angle of 60.0 degrees EAST of NORTH: The Dx component and the component of the vector are

A displacement vector D is given as 40.0 m at an angle of 60.0 degrees EAST of NORTH: The Dx component and the component of the vector are



Answers

A position vector has a length of $40.0 \mathrm{~m}$ and is at an angle of $57.0^{n}$ above the $x$ -axis. Find the vector's components.

All right, Welcome back. So for this problem, we have three different vectors and meet me to find which two of them are the same. So our first vector sector A as a critical component. 16 meters horizontal components of 80 meters. Yeah. Um, our second victor Victor be has the magnitude of 75 meters in ex complaint of 60 meters. Your last comport our vector. See, it was the night and into the 100 units for 100 meters performs an angle of 36.9 degrees with the x axis. All right, it's a 1,000,000 that, um we can see that first off, right from the very start in magnitudes of these two Vector inspector being being Excuse me, Victor, be in better. See are different. Right? What has the magnitude of 75 units And the other one has a, uh, magnitude of 100 uh, meters. So Oh, really? Ready to start? We can begin to see that it's looking like it's going to be either, um, Air, sea or Air B. Of course, if we Then we look at the X components, we can eliminate it being A and B, because the extra important of a is 80 meters and the X component being 60 meters. Yes, We're gonna do one calculation here just to verify that the vectors that are equal to each other really are the vector A which has these this x and Y components right here in the vector. See where we're giving the magnitude and the angle. So to verify this, you go about it several different ways. We could verified the the magnitude of vector a right here or refined Well, the ex compartment or Wycombe point of that. You see right here, we'll do it, Uh, the second way. So we're going to, um, to find the ex compliant right here of Victor. See, we're going to use co sign, but 36.9 degrees. And since the magnitude is 100 meters were going to skillet by a factor of 100 meters, not will give us, remember that it's quite nearly 80 meters. So there we have it. We have verified that it really vectors, eh? And the victor, see, are the same Victor. All right. Good luck on the rest of your homework.

In the execution. We have given a position vector whose ninth is 40 m. And it makes an angle of 57° from XX is so the vector can be looked at as to it were a triangle Director infusion would be the hyper 10 years. So first of all I'm drawing the triangle. This is triangle in which hyper tennis is our position vector. Both land is given to us. Let this is C. This length is A. And this is the That this triangle is eight b. See so in triangle A. B. C. Length of the position vector C. Which is 40 m. an angle Is given to us that is 57°.. This angle is 50 chairman degree And this 90'm. Now we have to calculate the component of this position vector. So first I am calculating the component. Yeah. So to calculate this we see that sign 57 degree can be written as abe. I see. So from here is witness Street Sign 57. Now put the value of C. Which is 40 And this is sign 57. After solving this we get the value of a. Which is 33.6 Metre. No in trying them again. In triangles. A. B. C. Big can write that course. 57 degrees can be written as B. Bye. See from here we get the which is C. Cause 57. Now put the value of c. That is 40 and 4th 57. After solving this we get the value of the that is 21.8 m. So in the given fusion our components are 8 33.6 metre And these 21.8 m. So this is the required come vectors component. Thanks

A vector is 20 m long at an angle 60 degrees counterclockwise from the Y axis. Given this information alone, we want to determine the X and Y components of this vector that is. We want to find both the length X and Y and whether or not X and Y are positive or negative. To start off, let's draw this out. So from the typical unit circle angle we have a 20 m vector that is 180 degrees from the X. Axis or the positive X axis. As you say. So from there, we can use the component method in order to figure out the X and Y components of this vector. So for X we have X. Is equal to co sign 103 times 20 plugging in 1 50 into the coastline. Function on a calculator multiplied by 20 gives us negative 17.332 m or the X. Length is 17.32 m to the left. Then, for why we have signed 1 50 times 20 Doing the same steps, gives us 10 m north or upwards.

All right. Welcome back today for a problem. So draw first. That coordinate playing here you got four vectors. Each of them points along an axis of the the Cartesian coordinate system for a first vector points due east and has a magnitude of Jew kilometers two kilometers 2nd 1 points due north. It has a magnitude of 3.75 kilometers. The next one points to your east and hunted in magnitude of 2.5 commoners in the last one when's due south met magnitude of three kilometers. So we can find the results in Victor are by taking the components of each of these vectors and adding them up. So let's seek first the ex components of all the vectors or your ex blue right here. So the X component ex components. Um so these two vectors right here do not to have any ex components. This one has a negative x compliant. This one has a positive X component. So a lot these defectors together and see what we get. We have two kilometers in the positive direction. The plus a negative 2.5 kilometers of the negative directions or just right minus 2.5 kilometers in the negative five direction in the negative, uh, ex direction. Excuse me, And that will give us negative 0.5 kilometers, which means that it's going to be heading in the west direction. If this were if this were a compass rose right here, all right. The white components were going to do something very similar. We're gonna use the other defectors now. Thes directors without white components. These defectors were here. Do not. So that is why we're gonna do that way. Um, do you have 3.5? Excuse me? 3.75 kilometers in a positive direction and in the negative direction. We have three commoners. It's a secret a 0.75 kilometers in the north direction, because this is positive. All right, sir, Victor is going to look something, something like this. All right, Victor are right there. Okay. So to find the magnitude of that factory recon used by tiger in the room, the magnitude of Victor are This one is equal to the square root of the X component squared, plus the white combined squared, which, if you plug that into your calculator, you'll find that the magnitude is equal to went 901 kilometers. The direction can be found using the tangent. Were to turn this into a train will reach here from this trying right here would have and see. I would have a length of 0.5 kilometers right here and a height of 0.75 kilometers. So that means that the tension would be the side opposite the Excuse me, the English theater. Right here. We're be beside opposite of that angle with the site adjacent that angle which plugging that into your calculator, you'll find that that is equal to 56 went 31 degrees north of west. All right, so there are your answers right there and there you have it.


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