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Worksheet2_Solutions

Worksheet2_Solutions - Vt lob\l'l‘y “I?o\‘ “M...

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Unformatted text preview: Vt lob \l'l‘y “I ?o§\‘+“M Lu/vf- Math 1920 Worksheet 2 1) The position and velocity curves of the problem just discussed are plotted below. The velocity curve has some asterisks that denote specific t values. Approximate where the corresponding position asterisks should be for each t value. t=[0.29|l +4w3t’a +9 4 Y o 2'} V = 4". L") 71—‘3 >. -2 u 45 6') Y 3) — a ’ k 4 ~45 -8 45 X 2) Aparticle moves alongan ellipse [111(5):] in the yz —-plane in suchaway that the 3 2 position vector is given as follows: r= 3cost j+ 2sint k Find the max and min values of |17| and |E|. (Hint: find max and min of |17|2 and Ialzfirst.) v : -3mt 5 +2¢bbtlz 32 —3wsts—2s~-«+»I< Z ogf: am“: .- H .os'i less": a “at +I—u smt Fx‘ad ”What 9+5 7. 4— AM“ GLUE; = 45mm 4' ’8 amt?“ ' 2 t8 sxht Lost " BuoS'tSW-‘t at V“? y: ‘10 ,‘mt cost: =0 (Osuntcost =0 - t:— 0111', 3' , 311- 11- 3T!“ 7 7‘ '2- Lf!‘+t¥nfl\ P-l—s t ' OITr; E J :‘ flus \'f\ t t m I 9. \ 0 2 $ x 11’ Z 3 I 2. 3 2 3E 2. 3 2’ 3) The curve 1' = < cos t, sin t, 1 — cos t > with 0 S t 5 2% is an ellipse formed by the intersection of a right circular cylinder and a plane. a) Find equations for the cylinder and the plane. FVAA z avg-Fox’s .‘n $31». me. ,Q ¢,\l\’9s¢ w'm 3 ‘94-5 at“ Lurvt. 1!; JR t“ “1’9““ ‘3‘“ 3 02"” A : P62 a?!“ Luau» fix tz'n' 610m, 2-37 $72, = 4-: ,I,1> “NM“ ”um a" P'“"‘ x :1: RC 01'] '3 + ‘ E “‘5 ' \' [A 9‘ ‘1'" ‘ ‘ oy’WWO‘Pr“ g'G V‘om)\utS i w, V‘ ‘3 3 Pwat as] warm and v) = LL. 0, 2,7 .‘HAroubk P ‘ ~ ‘ .— 5 2.(><-\\+<3+z(i-03=o M m 7‘ b) Show the acceleration vector always lies in the plane of the ellipse. ,. A saint! cost, Sl’At> K: n L -¢.astl - 5"fi't, cut.) 19 u 9 ‘ V‘ = (-1.05 t] ~$W\‘t’) Lu$t> ‘ L 2,0, 17 I ’ 2 cost "' Zoost 2 O _='> 9; _L G =. .‘A may“; 0'? cl‘i'Pfc, H c) Write an expression for the perimeter of the ellipse. p 11‘" U Sf. Farzge'i'cn‘teé af¢.\¢»n3 Pk EL L = 5 t :1 ml .5 t a 1/1- 1 : g «( Skr‘fi’z'é/A- (.0 t b$ihtt3 At ...
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