ENGR 233 Term Test 1 - Teacher: Suraj Joshi - Summer 2021 PDF

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Summer  2021  Concordia UniversityDepartment of Mechanical, Industrial and Aerospace EngineeringENGR 233: Applied Advanced Calculus**Term Test  1 ****Tuesday,  01  June  2021 Duration:  1  hr Maximum Marks:  **Note: All questions are compulsory ...

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Summer2021 ConcordiaUniversity DepartmentofMechanical,IndustrialandAerospaceEngineering ENGR233:AppliedAdvancedCalculus TermTest1 Tuesday,01June2021

Duration:1hr

MaximumMarks:50

Note:Allquestionsarecompulsoryandcarryequalmarks. Q1.Findtheanglebetweenthelines: ʆ : ʆ :

𝑥2 𝑦4 𝑧6   5 3 4 𝑥6 𝑧  11  𝑦1 3 2

Q2.Findthetangentialandnormalcomponentsofaccelerationandthecurvatureforaparticlemoving onthecurve𝑟󰇛𝑡󰇜  𝑡  𝚤  󰇛𝑡   3󰇜𝚥  󰇛𝑡   5󰇜𝑘 .Describethenatureofthecurveinwords.

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Q3.Let𝑧󰇛𝑢, 𝑣󰇜  𝑢 𝑣  𝑠𝑖𝑛 𝑣.Findand intermsofxandyonly,if𝑢󰇛𝑥, 𝑦󰇜  󰇛𝑥  𝑦󰇜 and 𝑣󰇛𝑥, 𝑦󰇜 

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. 

Q4.A4 𝑓𝑡tallchildthrowsatennisballatawall30 𝑓𝑡awaywithaspeedof44 𝑓𝑡/satanangleof60  abovethehorizontal.Whatistheheightfromthegroundandthespeedatwhichtheballhitsthewall?

󰇍 𝑓andcurl𝑣. Q5.Let𝑓󰇛𝑥, 𝑦, 𝑧󰇜  𝑥𝑦 – 𝑦𝑧and𝑣󰇛𝑥, 𝑦, 𝑧󰇜  3𝑧  𝚤  󰇛𝑥   𝑦  󰇜𝚥  𝑦 𝑘.Finddiv∇...