5

Name: InstructorDate Submitted: Section:PROBLEM SET # 1: INTRODUCTION TO VECTOR ANALYSIS On the space provided, present correct and organized solutions to the follo...

Question

Name: InstructorDate Submitted: Section:PROBLEM SET # 1: INTRODUCTION TO VECTOR ANALYSIS On the space provided, present correct and organized solutions to the following answered problems Box the final answers Detach each page neatly and submit to your instructor.Vector 20.00 km southeast; B is 14.00 km west € is 12.50 km 358 W of S, and D is 15.00 km 58" N ofw the resultant R is R =4 B+C +Dfind the ~component of R; and (Ans: Rr = -14.98 km) component of R: (Ans: Ry -11.66 km) What is the

Name: Instructor Date Submitted: Section: PROBLEM SET # 1: INTRODUCTION TO VECTOR ANALYSIS On the space provided, present correct and organized solutions to the following answered problems Box the final answers Detach each page neatly and submit to your instructor. Vector 20.00 km southeast; B is 14.00 km west € is 12.50 km 358 W of S, and D is 15.00 km 58" N ofw the resultant R is R =4 B+C +D find the ~component of R; and (Ans: Rr = -14.98 km) component of R: (Ans: Ry -11.66 km) What is the magnitude of the resultant? (Ans: R = 18.98 km) At what angle and direction is the resultant pointing to? (0 = 37.908 $ ofw Aoco; 4S + -14 Fia,s1n35 15 (0151 Cos 35 91n 58 1051045 10 66ko kule un Ry Wm 14,48 37,90*5



Answers

Solve Problem $1.8$ by use of rectangular components. We resolve each vector into rectangular components as illustrated in Fig. $1-12(a)$ and $(b)$. (Place a cross-hatch symbol on the original vector to show that it is replaced by its components.) The resultant has scalar components of $$ s_{x}=1.53 \mathrm{~m}-2.41 \mathrm{~m}=-0.88 \mathrm{~m} \quad s_{y}=1.29 \mathrm{~m}+3.19 \mathrm{~m}=4.48 \mathrm{~m} $$ Notice that components pointing in the negative direction must be assigned a negative value. Thus, since $s x$ is to the left in the negative $x$ -direction it is negative, whereas sy is upward in the positive $y$ -direction and is positive. The resultant is shown in $\underline{\text { Fig. } 1-12(c) \text { ; there, }}$
$$ s=\sqrt{(0.88 \mathrm{~m})^{2}+(4.48 \mathrm{~m})^{2}}=4.6 \mathrm{~m} \quad \tan \phi=\frac{4.48 \mathrm{~m}}{0.88 \mathrm{~m}} $$ and $\varphi=79^{\circ}$, from which $\theta=180^{\circ}-\varphi=101^{\circ} .$ Hence, $\overrightarrow{\mathrm{s}}=4.6 \mathrm{~m}$ - $101^{\circ}$ FROM $+x$ -AXIS; remember, vectors must have their directions stated explicitly.

Hi for this question, I want to find the result of the force in this figure. Using the component method. So, first of all, it's um we're going to result each of these forces. Therefore, forces. They were going to resolve them into their vertical and original components. So where's your triangles? Around these? And for And what they can be positive direction as right and up. So hope is positive, right is positive and down is negative. Left is also negative sort. Let's start with the original component. So the reason for this 110 Newtons will be the 4th year. And there is something that is in this you're gonna magic races. We have Cost 32 110. Of course that changes in the negative direction to the minus going left. And for the vertical for this same force 2110 sign. Did she Now for the next 4116 year change this would be -160 cost 20. This is -116 Showing 20 because this is going down left, which are both negative. And the next one, let's go to the 18 years in this one only has a regional company into the critical comments of his era. And just want to be 80 newtons because it's going to positive. So this plus and then for the 100 newtons, the vertical horizontal, both positive. So this is 100 mm of course 45 And 100 sign 45. And our total for each of these would be Negative, or nine mutants. This is 71 point their attention. So for the resultant f Be called to using the Pythagorean theorem described of -94.9. All squared Plus 71.0 Squared. Listen be equal to approximately 1 20 Newtons. And this this is too significant figures. So um next to find a direction we want to use theater. Did you go to turn inverse of vertical? Valuable? The horizontal? So 7 to 1, Write it by -94.9. And this beagle two -36.8 Newton's. And this negative sign means that is below the X axis. So we have the Y here at the X. Have an angle of 36 point each year. So it wants to fight is this angles going counterclockwise And we do 3 16 rather. Well, let me try this again. What's that? So what we found was the horizontal is -94.9. So this would be in left direction And we got 94.9. And we have the last positivity so it's one point, sir. Yeah. So our uncle has to be somewhere between these and So quickly did as minus that six point. It's just to be 13 point. It's from the horizontal. Sure. So what we need to do is find this direction and we're doing nightie rather these old places wanted to so I didn't want it to 1 80 degrees. Okay, I'm just playing that little, mm hmm. So this whole place is wanted to see. You don't want to t minus statistics. Point it. And so angle there, that would be Approximately 1 4-3 went to degrees. And so these are direction and our force magnitude rather.

Hi this question. We have this diagram and want to find the resultant graphically. So all we need to do is join the forces and to end. And then the result will be Mhm. A foster takes it from the starting point directly to the ending point. So let's try this. We can start raining force. Start from the bottom 80 newtons To have 80 nations. Yeah. And then because we can go to the next one, 100 newtons, 100 Nilson's, Then this next one, wow, one drink. Then Newton's then to this one. 160 Newtons. Okay. And so we have the result of us here from here to this point directly from the starting to finish to the end point. So we're doing a lot of these. We need to put some directions and a protector and draw the directions perfectly. So when you measure this angle, you have the correct uncle and you also have the correct magnitude for the lamp. Okay, so for each of these, you can use it centimeters for each newton's and you can use 10 centimeter, 200 newtons, 11 centimeters. 1 10 newtons. and 16 cm for 1 16 years is so when you measure this side. So this angle will be 45° here and Also the angle of 30°. This past 20°. So we measure the side, we have a length of 119 centimeters which would be equivalent to 19 year tens and measuring the angle of the pro crypto This child would be one for today, decrease. So the resultant Would be 119 Yeah, tunes the direction uh 1 43 degrees from the horizontal. Yeah.

All right. So this problem is all about vector edition. And so the steps were a problem like this are always going to be number one, you always have to draw a picture first. So you can visualize the vectors. Number two. Split each vector into their component vectors. Number three for this one, you're gonna have to solve some of equations. So on the right here have a picture drawn out. Doesn't need to be like totally exact with the ankles and the lengths, but just a general idea of what the vectors look like. So we know that the they start and end in the same place. So the end of vector C. Is the same as the beginning of the vector A. And then on the right, we know that we have what we know which is the magnitude of vector A. Which is 145. And then what we're looking for which is the magnitude of vector B. And the magnitude of vector C. Yeah. And so next we have to split it into their component actors. So I have a little example here showing how to split into component vectors. And it's also why the picture is important because we need to know from what direction the angle is located. Okay. Social vector I want to split it into the excellent my components. The X component is going to be its magnitude. There's 145 times a co sign of its angle which is 35. And the Y components can be man 245 times the sine of 35. Yeah. And then for the components of B we don't know the magnitude. So we'll just call the magnitude be and it's going to be negative because this is the X component explains negative because it's opposite traveling in the opposite direction of A's X. Component. She is going to the left and bees going to the right. So negative. Big times a sign of 65. And we know that again from the picture that we drew and then the Y component we're gonna be positive because it's traveling up just like the A. Component. So and then again the magnitude of B. And co sign 65. And again we don't know the magnitude of vector C. So we'll just call it C. And that's the X component is going to be signed 15 degrees. Yeah. And the Y component is gonna be negative because it's in the opposite direction of the A. A vector. So negative C. And the co sign of 15. Okay. And now that we have it into their component vectors, we can use this equation right here. Which we get because the vectors starting to end in the same place. So the result in vector is going to be zero mm. And so from this we can we also know that each of the X components X plus B, X, C X also equal zero and same with the Y component. So A Y plus B, Y plus C, Y equals zero. And from these two we have two equations and two unknowns which is the magnitude is of B and C. And so here, I've already plugged in that excellent Y components into these two equations and then we just saw the system of equations. So we isolate one of the variables in this case. I did see and then we plugged that in so we have an equation with only B equals zero. And then we can just solve for B, which in this case it becomes 178 0.56 And then we can plug that in to our equation for C. And we can sell for seat, which is 164.2. So there are two magnitudes for the vectors B and C. And again, just to reiterate the most important part of the vector addition problem is always drawing the picture. Yeah. Mhm.

So this problem wants us to make a scale diagram of the pilots motion and use this diagram to obtain the magnitude and direction of the resultant vector and then compare it with the answers that will be obtained using component method to solve for magnitude and direction. That is authentic. I suppose these are, sorry, ruler. Then let's promote this point after this point as one. Yeah the nurse scale is one is equal to $100 billion dollars and let upwards be door. The right side is east downwards is south and left. The swiss it said that vector A has a magnitude of 244 kilometers and the direction is 30 degrees north of east which means 30 degrees from east towards no north. So you still move a ruler this week. This is 30°. Then we have for vector A. Which is Then the magnitude in our scale is 2.44. So we have this one then this is two. So this is 2.1 .2, and almost on the middle is two points 44. So this is our backdoor. A way to manage funny. No, for vector B. It is stated that It is one that is 75 km due west So are scaling is 1.75 and towards the left side then we have why 1.12 34567 in the Middle East, 1.75 one. So this is why 75. Now the resultant vector is the distance from the head of dr A. Andy I mean that starting point of vector A. Which is the thing to head of vector B. Yeah. So from here. So as you can see this is our angle. Yeah. Then we have the Angle result and anger direction of the resultant vector is 74, the grease. And for the magnitude it is the length so you have to call it. Then we have one 1.1 1.2 and That's not 1.3 let's say around one 27 up to here. Yeah. Remember to this 1.27 or 127 km now Greater than eight us. Which is greater the magnitude the magnitude of that there's A or the factor are so as you can see are Yes, less than but they're eight Which is started 44 km and victor beast 97 different kilometer. So our is less than 244 kilometers are less than eight gradually beat us. Which is creator vector magnitude of vector B or months. You are So the results and also you can see are also less than vector B. You guys didn't see us is the direction Greater than or smaller than 30°. So the answer is data Yes. Good. A. 3rd. Done. 30 degrees. Okay. And the direction is north of is no let us use component method to confirm his answer. We know with the magnitude of art is equal to this square root of it square definite Horizontal and vertical components where our x equals two A X. B X in ry equals two A. Y. Last B Y. For a It's percentile component is 2044 km, modified by Carson 30 degrees. And for B since it's purely vertical, I purely horizontal, I mean And due to us then it's horizontal component is negative 175 km. And for our y we have 244. Do you love me Through since you two? It is north of So as you can see it is 244 kilometre crossing 30 biggest positive for horizontal and for the vertical it's also positive since it is 30° below where it's not. So applying for tubercular meters, signed 30°. And since vector B is purely horizontal, it has no vertical component. So this is zero. And so being we can find that Our x equals to Turkey six km and RY is equal to 122 km. Then solving for our we have squared off 36 kilometer quantity squared plus 122 kilometer quantity screwed solving you can find that is close to 90 27 kilometre borda angle. We know that it is the formula tangent inverse of the opposite side over the ridge. Inside is our white over our X. So what value? This is indicates absolute value. Then we have tangent inverse of By 1922 km, over 36km. And we can find that this is equals to 74 the grease. And since both ours and our by positive, then that direction is not uh which agrees with our resort using the scale diagram.


Similar Solved Questions

3 answers
Problem 2. (20 points) Consider the following matrix A: r0 8Obtain Matlab results of eigenvalues of A. Then obtain the transformation matrix P such thatP-'AP = diag(11,12,13,A4)
Problem 2. (20 points) Consider the following matrix A: r0 8 Obtain Matlab results of eigenvalues of A. Then obtain the transformation matrix P such that P-'AP = diag(11,12,13,A4)...
5 answers
Weterminaticn #f Molur Muss by Frceeiog Polnt DcpreacionData:Mass of cmply lCst tube206 Mass tcst tubc plus approximately 10.0 of benzophenone 33228 The diflerence is the mass of benzophenone (solvent) Mass of unknoun (~[.0 g) 1.9 Freezing point of pure benzophenone kr Soc Freczing point of benzophenone containing the unknown 420& 2 Thc differencc is 4 fpCalculations: (Shov sct-OP with concellation of uniis)molality of solutionmnolet of solute usedoarmaee
Weterminaticn #f Molur Muss by Frceeiog Polnt Dcpreacion Data: Mass of cmply lCst tube 206 Mass tcst tubc plus approximately 10.0 of benzophenone 33228 The diflerence is the mass of benzophenone (solvent) Mass of unknoun (~[.0 g) 1.9 Freezing point of pure benzophenone kr Soc Freczing point of benz...
4 answers
Which dataset would be most appropriate to use a histogram to graph? Tests given per section of Statistics Graduates from a psychology program by year Time taken to complete a statistics test Psychology professors by university
Which dataset would be most appropriate to use a histogram to graph? Tests given per section of Statistics Graduates from a psychology program by year Time taken to complete a statistics test Psychology professors by university...
5 answers
Calculate the magnitude of the Resultant of vectors the three Band € shown; given that: A =160 B = 140 C =190450 30970.576.672.874.961.9
Calculate the magnitude of the Resultant of vectors the three Band € shown; given that: A =160 B = 140 C =190 450 309 70.5 76.6 72.8 74.9 61.9...
5 answers
TniSivm.usletoidEmnpbcol orblt about thesun travck & 24 18 ms Lcbatetniheh ChEITA IEulGunleceritellonCtala Bednadiantntontust & Etuyoing ot Jpheion
Tni Sivm. usletoid Emnpbcol orblt about thesun travck & 24 18 ms Lcbatetniheh ChEITA IEulGunle ceritellon Ctala Bedna diantn tontust & Etuyoing ot Jpheion...
2 answers
(Type . The area Find the of the area H 8 using surace Tas needed ) generated by revolving generated 2 revolving 1 the 42x curve y 42x 07667615 about the Kaxt about the xarie 0 Wils:
(Type . The area Find the of the area H 8 using surace Tas needed ) generated by revolving generated 2 revolving 1 the 42x curve y 42x 07667615 about the Kaxt about the xarie 0 Wils:...
5 answers
Calculate the pH of each buffers:0.Q4OQM Tris + 0.O6QQM Tris HCL [(Tris= tris (hydroxymethyl) aminomethane]01M CHBCOOH + 01OQM (CH3CO2)2Ca
Calculate the pH of each buffers: 0.Q4OQM Tris + 0.O6QQM Tris HCL [(Tris= tris (hydroxymethyl) aminomethane] 01M CHBCOOH + 01OQM (CH3CO2)2Ca...
5 answers
105284311uddHSP-00-528
10 5 2 8 4 3 11 udd HSP-00-528...
5 answers
We wish to test the hypothesis H0 : p=0.64. For a sample of size 40, the sample proportion P is 0.55. Compute the value of the test statistic zobs. Express answer rounded two decimal places
we wish to test the hypothesis H0 : p=0.64. For a sample of size 40, the sample proportion P is 0.55. Compute the value of the test statistic zobs. Express answer rounded two decimal places...
5 answers
13 Arrange in order of _ decreasing acid strength: HC=CH HzC CH H;c ~CHy [ II A. I> M>M B, M>I>[ C I>M>M D. M>I> D E. M>I>M
13 Arrange in order of _ decreasing acid strength: HC=CH HzC CH H;c ~CHy [ II A. I> M>M B, M>I>[ C I>M>M D. M>I> D E. M>I>M...
5 answers
In each case determine the region in R? at which the partial differential equation is Parabolic Elliptic or Hyperbolic and Sketch the region6x2 +y2)? uxr 4xy Uty + Uyy(ii) (1 +y)uxt 2 2+xy2 uxy + (I+x2) Uyy Sy u, 9x Uy 17 u =(iii) (x ~ 3y) %w 6 @w am Ox? Oxoy (x + 3y)
In each case determine the region in R? at which the partial differential equation is Parabolic Elliptic or Hyperbolic and Sketch the region 6x2 +y2)? uxr 4xy Uty + Uyy (ii) (1 +y)uxt 2 2+xy2 uxy + (I+x2) Uyy Sy u, 9x Uy 17 u = (iii) (x ~ 3y) %w 6 @w am Ox? Oxoy (x + 3y)...
5 answers
# IkxitbairirQuestian_ points) # T4#{kxin % gi5"i3rj4?'eicuu AadeI Elct
# Ikxit bairir Questian_ points) # T4# {kxin % gi5"i3rj4? 'eicuu AadeI Elct...
5 answers
{7 171 4 1
{7 17 1 4 1...
5 answers
Come populations The 1 Behavioral H Question = Isolation Iul H onthef sthish Isthmus = This W million V ago V even gene between Atlantic and flow they were again between Atlantic Pacific fish pue 2
come populations The 1 Behavioral H Question = Isolation Iul H onthef sthish Isthmus = This W million V ago V even gene between Atlantic and flow they were again between Atlantic Pacific fish pue 2...
5 answers
8. Draw the mechanism of the reactions below:McOHH,o'hoatNallIdentify each R group of the ether as the alcohol or alkyl halide for the Williamson ether synthesis of an ether: Provide an example of each
8. Draw the mechanism of the reactions below: McOH H,o' hoat Nall Identify each R group of the ether as the alcohol or alkyl halide for the Williamson ether synthesis of an ether: Provide an example of each...
5 answers
0 0,24 N0 5.6N12N92N6i.2N
0 0,24 N 0 5.6N 12N 92N 6i.2N...
5 answers
Give the major organic product of the reaction m3 PBrzHO"
Give the major organic product of the reaction m3 PBrz HO"...

-- 0.020368--