SOLUTION: ENGM 2101 Dalhousie Universit yApplied Vector Calculus Quiz Questions

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Dalhousie University Department of Engineering Mathematics ENGM 2101 Applied Vector Calculus Summer 2020 Quiz #1 Faculty of Engineering Academic Uprightness Proposition for Inclusion in Exams This is a explicit proposition of commitment to academic uprightness for impost in ENGM 2101 Applied Vector Calculus Summer 2020. Students are asked to corroborate their commitment to the principles of ethics, uprightness and professionalism embedded in this proposition as it is an expectancy of all novices and homogeneous weighty, an expectancy of you during your coming walk as a Professional Engineer. Expectation of Student: The exam is to be accomplishedd partially by the novice. Specifically, novices are not to discuss the exam behind a while others or cooperate on the substance of the exam behind a while others, including other students in this series, in any habit. Students are expected to flourish the instructions on the exam and use singly the series symbolical or instrument as exempt. A commitment to a high standard of separate uprightness and professionalism is expected of all engineers and is homogeneous expected of those inaugurated towards a walk in engineering. Certification By yieldting this product, I avow that the product represents singly my own efforts and was completed in a habit agreeing behind a while the instructions supposing. I corroborate that I comprehend the meaning and consequences of imposture, plagiarism and other academic offences beneath the Faculty Discipthread Procedures for Academic Dishonesty , and am conscious of my responsibilities beneath the Intellectual Honesty Policy . 1 Instructions Specific to This Quiz • • • • • • • • • • • • • • • This satire is beneficial from 11am Tuesday May 12th until 11am Wednesday May 13th. The satire is contrived to be accomplishedd behind a whilein 2 hrs, but you may exhaust further or hither time as you appropriate, position in liking that your exculpations must be uploaded to Brightquantity by 11am Wednesday May 13th. Enstable your designate and ID are on your dependence, and that all your pages are comprised in the unmarried muniment you yield. Please yield your exculpations as a unmarried *.pdf or *.docx perfect, which can, for specimen, be generated from photos or scans of your handwritten pages, or apps that let you transcribe on a tablet and astern obviate your notes to a perfect. There is ostensible a unimpeded phone app called CamScanner that a novice has recommended as advantageous in getting your notes prepared for dependence. Be stable to click yield to obviate your perfect in Brightspace. You should take an email confirmation of your lucky dependence. You enjoy an unbounded sum of dependences, but singly the unmarried perfect representing your most novel dependence procure be graded. Please enstable your handdespatches is wheedleigraphic and your exculpations are logically organized. If the grader cannot unravel what you wrote, or cannot flourish what you did, you procure not take reputation. Students procure be despatches the satire at irrelative times. Thus, for candor, to enstable everyone is supposing the identical counsel, no questions procure be exculpationed during the satire. While not required to accomplished the satire, you are agreeable to advert to your notes, the series symbolicals on Brightspace, and/or the textbook. Attempt all 5 questions There are a aggregate of 55 subject-matters The subject-matter appraise of each question/sub-question is ardent in parentheses If you get store, establish an certainty, propound it, and proceed Partial reputation may be ardent for inexact exculpations that prove punish method Show your product – no reputation procure be ardent for exculpations behind a whileout adapted justification 2 Question 1 (1 subject-matter each = 10 subject-matters aggregate) State whether the flourishing are frequently penny (T), frequently sham (F), or there is not enough counsel to establish the vill (N). ( ) ! ! a) r1 (t) = ( cos(3t),sin(3t) ) and r2 (t) = cos(t 2 ),sin(t 2 ) portray the identical flexion for t ≥ 0 . ! ! ! b) The tangent thread for r (t) at the subject-matter t = t0 is ardent by (x, y, z) = r (t0 ) + k r ′′(t0 ) , where k is a scalar. ⌢ dTˆ dTˆ c) Ardent T (s) , where s = f (t) , then and are correlative. ds dt d) The part regular N̂ is orthogonal to dN̂ . dt ! e) The concatenate of soaring for a missile that is instituted from the reason behind a while a quickness v is longer than the concatenate of soaring of a irrelative missile that is instituted from a culmination h over the reason behind a while the identical quickness. ! f) The interval concurrently r (t) betwixt a ≤ t ≤ b is shorter than the majority of displacement ! ! betwixt r (a) and r (b) . g) There is a element of aid that is correlative to the part binormal. h) The tangential element of aid represents the rate of diversify of address. i) The utmost inflexion of a missile’s trajectory occurs at the utmost culmination of the projectile. j) The torsion of a helix is cipher. Question 2 (9 subject-matters) a – 2 subject-matters) Ardent that a atom starts at P0 = (2, 1, 1), voyages in a right thread and gets to P1 = (-1, 0, 4) behind 1 cooperate, and it continues concurrently the identical thread at the identical hurry, where procure the atom be 2 cooperates behind it passed P1? Question 2 continued on the next page 3 b – 2 subject-matters) Select the discretion that portrays the quantity flexion shown beneath ( ) ( ) i) ( acost,asint,bt ) , ii) e at require,e at sint,bt , iii) ( bt,acost,asint ) , iv) bt,e at require,e at sint , or v) none of the over ⎛ t 2 −t 3 ⎞ ! ! c) Two atoms voyage concurrently flexions r1 (t) = ⎜ t, , and r1 (t) = 22 − 3t,2 + t,4 − 2t both ⎟ ⎝ 2 8 ⎠ beginning at t = 0. The trajectories iteme at the subject-matter (4, 8, -8), but the atoms do not collide. ( ) ! i -- 2 subject-matters) Ascertain the equation of the tangent thread for r1 at the subject-matter of itemeion. ii -- 3 subject-matters) Ascertain the inclination at which the two flexions iteme. Question 3 (6 subject-matters) ! a) Ardent a atom is on the trajectory r (t)= ( sint,cost,sin(2t) ) for 0 ≤ t ≤ 2π , i -- 2 subject-matters) Ascertain an countenance for the hurry as a employment of time ii -- 2 subject-matters) Determine the utmost hurry of the atom. d ! ! ! ! ! ! r (t) × v(t) ) = r (t) × a(t) , where v(t) is the quickness, and a(t) is ( dt the aid, and excuse your exculpation. b -- 2 subject-matters) Propound whether 4 Question 4 (11 subject-matters) ( ) ! ! a -- 3 subject-matters) Ardent an aid a = 1,e2t ,4t and judicious quickness v(0) = ( 2,1,0 ) , ascertain the displacement betwixt t = 0 and t = 1. b -- 4 subject-matters) A wildlife conservationist wants to inspirer a tranquilizer fly at an endangered monkey sitting at the top of a 20m tree, which is 80 m abroad. She knows the monkey procure faint from the tree the force the gun is inspirerd, and boon her gun accordingly. Ardent that the stop quickness is 100m/s, ascertain the culmination at which the fly hits the monkey. ( ) ! c -- 4 subject-matters) Ardent a atom voyages concurrently the flexion r (t) = t 2 , 2t, lnt , ascertain the interval traveled for 1 ≤ t ≤ 2 . Question 5 (19 subject-matters) a -- 3 subject-matters) For the flexion shown beneath, outline the part tangent, Tˆ , and part regular, N̂ , vectors at the two subject-matters implied (where t1 Purchase exculpation to see full attachment

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