.MCAD 306000000 Z  docDocument<mcObjectIÿÿÿÿ““ d2_graph_format graphData axisFormatLLtrace2D      dim_formatCmasslengthtimecharge temperature luminosity substance°Š'€NumericalFormat@dii shpRectE mcDocumentObjectStateJð´ mcPageModel:š™™?œ?š™™?š™™?mcHeaderFooter99 ComputeEngine=BuiltInsBy SerialAnyvalH@z@H @{@H|@Hü©ñÒMbP?}@H units_classA TextState0 TextStyle/@ArialNormalÿÿÿÿÿÿÿÿ€font_style_list> font_style?ðÿÿÿóÿÿÿ  VariablesTimes New Roman?ðÿÿÿóÿÿÿ  ConstantsTimes New Roman?îÿÿÿðÿÿÿÿÿÿÿTextArial?óÿÿÿöÿÿÿ ÿÿÿÿSymbol?óÿÿÿöÿÿÿ ÿÿÿÿUser^1Arial?óÿÿÿöÿÿÿ ÿÿÿÿUser^2 Courier New?óÿÿÿóÿÿÿ ÿÿÿÿUser^3System?óÿÿÿóÿÿÿ ÿÿÿÿUser^4Script?óÿÿÿóÿÿÿ ÿÿÿÿUser^5Roman?óÿÿÿöÿÿÿ ÿÿÿÿÿUser^6Modern?óÿÿÿöÿÿÿ ÿÿÿÿUser^7Times New Roman?ðÿÿÿóÿÿÿ Symbol?óÿÿÿóÿÿÿ ÿÿÿÿArial?óÿÿÿóÿÿÿ ÿÿÿÿ?óÿÿÿóÿÿÿ ÿÿÿÿArial?óÿÿÿóÿÿÿ ÿÿÿÿArial?ðÿÿÿóÿÿÿ Times New Roman& TextRegion docRegion7shpBoxD@í-@(‰­­­ CharacterMapRangeMap,$UNIVERSITY PHYSICS I COMPUTER LAB #1 ChrPropMap($ RangeElem-$  ChrPropData) RangeData.lArial0,128,0 ParPropMap*$ -$  ParPropData+EmbedMap" -LinkMap $ -$LinkData!ÿÿÿÿ@NormalArialÿÿÿ@DG2ÚX>8"“"“AdFirst we learn how to do simple computations with MathCad. (1) Type:3*4= The answer is: 12. (2) Type 24-35= The answer is -11 (3) Type: \3= (this is square root of 3). The answer is 1.73 (4) Type 2.3^4.5= (this is 2.3 to the power 4.5). The answer is 42.44 (5) Type: (3-4)*4-6= The answer is -10 (6) Type: 7/(2.3-8.6)space bar+3=. The answer is:1.889 (d*d-d+ÿÿÿÿÿÿÿÿÿÿÿÿ"- d-d!ÿÿÿÿ@NormalArialÿÿÿeqRegion3@D¨ðïÅKtree1 p1ŒÁ€1Ê@1t31´41–Ä€1+@Serial_DisplayNodeF1¤ _n_u_l_l_3@D¨%á J1 p 1ŒÁ€!1ˆÇ@ "1t!24#1´!35$1–Ä€ %1+@$@F&1¤$ _n_u_l_l_'3@D¨/MÂHI(1 p)1ŒÁ€(*1š{@)+1´*3,1–Ä€)-1+@,@F.1¤, _n_u_l_l_/3@D¨ZuÓpH01 p11ŒÁ€021ü@131t22.341´24.551–Ä€161+@5@F71¤5 _n_u_l_l_83@D¨€6•�G91 p:1ŒÁ€9;1ˆÇ@:<1Ê@;=1Žp@<>1ˆÇ€=?1t>3@@1´>4@A1´<4@B1´;6@C1–Ä€:@D1+@@C@F@E1¤@C _n_u_l_l_@F3@D¨•PðF@G1 p@H1ŒÁ€@G@I1‰Ç@@H@J1û@@I@K1t@J7@L1Žp€@J@M1ˆÇ€@L@N1t@M2.3@O1´@M8.6@P1´@I3@Q1–Ä€@H@R1+@@Q@F@S1¤@Q _n_u_l_l_@T@DçF¤øL@>½>½AîWe now learn to use vectors and matrices (arrays) with MathCad. (1) Open the Vextor and Matrix palette and click on Matrix and Vector button. Create two vectors a and b: 3 rows and 1 column. To assign the values to the vector a type: a: Then type the values. (2) Do the cross product axb by clicking on the correspondinkg button. (3) Do the dot product. (4) Calculate: a*(axb). Can you explain the answer. (5) Calculate the product of a scalar and a vector: c = -3a. What is cxa equal to? (íìî@U-ì@V)@T`Arial0,0,0@W-@X)@Tn Arial0,64,128@U@Y-@Z)@Tl Arial0,64,128@W@Y@U*î@[-î@\+ÿÿÿÿÿÿÿÿÿÿÿÿ"@]- î@^-î@_!ÿÿÿÿ@NormalArialÿÿÿ@`3@D´Eàd@a1 p@b1 Á€@a@c1d@ba@d1Žp€@b@e10Á�@d@f10ÁA@e@g10ÁA@f@h1@@g@i1´@g1@j1´@f3@k1•K€@e@l1´@k2@m3@Dh´²yàc@n1 p@o1 Á€@n@p1d@ob@q1Žp€@o@r10Á�@q@s10ÁA@r@t10ÁA@s@u1@@t@v1•K€@t@w1´@v0.3@x1´@s3.1@y1•K€@r@z1´@y2.5@{3@DÈ´1ðàb@|1 p@}1ŒÁ€@|@~12Ê@@}@1d@~a@€1¤@~b@�1–Ä€@}@‚1+@@�@F@ƒ1¤@� _n_u_l_l_@„3@DXОåtàa@…1 p@†1ŒÁ€@…@‡1Ê@@†@ˆ1d@‡a@‰1¤@‡b@Š1–Ä€@†@‹1+@@Š@F@Œ1¤@Š _n_u_l_l_@�3@DÐÐ4åà`@Ž1 p@�1ŒÁ€@Ž@�1Ê@@�@‘1d@�a@’1Žp€@�@“12Ê€@’@”1d@“a@•1¤@“b@–1–Ä€@�@—1+@@–@F@˜1¤@– _n_u_l_l_@™@Dˆ#<3ˆ0fд´copyright Miron Kaufman, 1998(@š-@›)@™n Arial*@œ-@�+ÿÿÿÿÿÿÿÿÿÿÿÿ"@ž- @Ÿ-@ !ÿÿÿÿ@NormalArialÿÿÿ@¡3@DhP}(xj@¢1 p@£1 Á€@¢@¤1d@£c@¥1Ê€@£@¦1•K@@¥@§1´@¦3@¨1¤@¥a@©3@DÈL œ×xi@ª1 p@«1ŒÁ€@ª@¬1d@«c@­1–Ä€@«@®1+@@­@F@¯1¤@­ _n_u_l_l_@°3@D€LÜœ§xh@±1 p@²1ŒÁ€@±@³12Ê@@²@´1d@³c@µ1¤@³a@¶1–Ä€@²@·1+@@¶@F@¸1¤@¶ _n_u_l_l_@¹@D¯%HÀl(™™A½We next study projectile motion. Set the constants: v0, theta (in radians) and g. Set the time interval by typing t: 0,0.01;1(meaning the first t is 0, the next is 0.01 and the last is 1). Define x(t), y(t), vx(t), and vy(t). To get a subscript type . period . For example: v.x(t) shows as vx(t). Graph the trajectory y versus x. Graph velocity components and position components versus time. Note that at the top of the trajectory vy = 0.(¸6½@º-6@»)@¹lArial255,0,0@¼-@½)@¹LArial255,0,0@º@¾-�@¿)@¹lArial255,0,0@¼@À-@Á)@¹LArial255,0,0@¾@Â- @Ã)@¹lArial255,0,0@À@Ä-@Å)@¹LArial255,0,0@Â@Æ- @Ç)@¹lArial255,0,0@Ä@È-@É)@¹hArial255,0,0@Æ@Ê- @Ë)@¹lArial255,0,0@È@Ì-@Í)@¹255,0,0@Ê@Î-@Ï)@¹_255,0,0@Ì@Ð-@Ñ)@¹255,0,0@Î@Ò-Œ@Ó)@¹lArial255,0,0@Ð@Ô-@Õ)@¹LArial255,0,0@Ò@Ö-@×)@¹lArial255,0,0@Ô@Ö@º*½@Ø-½@Ù+ÿÿÿÿÿÿÿÿÿÿÿÿ"@Ú- ½@Û-½@Ü!ÿÿÿÿ@NormalArialÿÿÿ@Ý3@D PYk<`“@Þ1 p@ß1 Á€@Þ@à1d@ßv.0@á1´@ß23@â3@DxEÅs‰`’@ã1 p@ä1 Á€@ã@å1d@ä\q@æ1Ê€@ä@ç1t@æ60@è1û€@æ@é1d@è\p@ê1´@è180@ë3@DàPeð`‘@ì1 p@í1 Á€@ì@î1d@íg@ï1´@í9.8@ð3@D0E�sB`�@ñ1 p@ò1 Á€@ñ@ó1d@òT@ô1Ê€@ò@õ1Ê@@ô@ö1t@õ2@÷1¤@õv.0@ø1û€@ô@ù1Î@@ø@ú1d@ùsin@û1Žp€@ù@ü1¤@û\q@ý1¤@øg@þ@D¸O@d¸`�°ˆˆT is time of flight.(@ÿ-A)@þ~255,0,0*A-A+ÿÿÿÿÿÿÿÿÿÿÿÿ"A- A-A!ÿÿÿÿ@NormalArialÿÿÿA3@D €|•-�qA1 pA1 Á€AA 1dAtA 1€AA 1 Ã@A A 1tA 0A 1´A 0.01A1¤A TA3@D ˜�³C¨xA1 pA1 Á€AA1Î@AA1dAxA1Žp€AA1¤AtA1Ê€AA1Ê@AA1dAv.0A1΀AA1dAcosA1Žp€AA1¤A\qA1¤AtA3@D˜‡³6¨wA1 pA 1 Á€AA!1Î@A A"1dA!v.xA#1Žp€A!A$1¤A#tA%1Ê€A A&1dA%v.0A'1΀A%A(1dA'cosA)1Žp€A'A*1¤A)\qA+3@D µÎãCÐzA,1 pA-1 Á€A,A.1Î@A-A/1dA.yA01Žp€A.A11¤A0tA21ˆÇ€A-A31Ê@A2A41Ê@A3A51dA4v.0A61΀A4A71dA6sinA81Žp€A6A91¤A8\qA:1¤A3tA;1Ê€A2A<1Ê@A;A=1û@A1tA=1A?1´A=2A@1¤A<gAA1ü€A;AB1dAAtAC1´AA2AD3@DÀ£Û6ÐyAE1 pAF1 Á€AEAG1Î@AFAH1dAGv.yAI1Žp€AGAJ1¤AItAK1ˆÇ€AFAL1Ê@AKAM1dALv.0AN1΀ALAO1dANsinAP1Žp€ANAQ1¤AP\qAR1Ê€AKAS1dARgAT1¤ARtAU3@D9!AV1 pAW1Á€AVAX1ŸÁ@AWAY1ŸÁ@AXAZ1ŸÁ@AYA[1fAZ 20.242316A\1¦AZ0A]1ŸÁ€AYA^1dA] _n_u_l_l_A_1¤A] _n_u_l_l_A`1΀AXAa1dA`yAb1Žp€A`Ac1¤AbtAd1ŸÁ€AWAe1ŸÁ@AdAf1ŸÁ@AeAg1fAf46.69Ah1¦Af0Ai1ŸÁ€AeAj1dAi _n_u_l_l_Ak1¤Ai _n_u_l_l_Al1΀AdAm1dAlxAn1Žp€AlAo1¤AntAp7 NXNY TRAJECTORY     Aq@DhS+ch`†ÃÃÃCopyright @Miron Kaufman, 1998(Ar-As)Aqn Arial*At-Au+ÿÿÿÿÿÿÿÿÿÿÿÿ"Av- Aw-Ax!ÿÿÿÿ@NormalArialÿÿÿAy3@D‡î¨ˆŽAz1 pA{1Á€AzA|1ŸÁ@A{A}1ŸÁ@A|A~1ŸÁ@A}A1tA~30A€1¦A~0A�1ŸÁ€A}A‚1dA� _n_u_l_l_Aƒ1¤A� _n_u_l_l_A„1 ÀA|A…1Î@A„A†1dA…xA‡1Žp€A…Aˆ1¤A‡tA‰1΀A„AŠ1dA‰v.xA‹1Žp€A‰AŒ1¤A‹tA�1ŸÁ€A{AŽ1ŸÁ@A�A�1ŸÁ@AŽA�1dA�TA‘1¦A�0A’1ŸÁ€AŽA“1dA’ _n_u_l_l_A”1¤A’ _n_u_l_l_A•1¤A�tA– NN     A—3@D0‡ ¨0ˆ�A˜1 pA™1Á€A˜Aš1ŸÁ@A™A›1ŸÁ@AšAœ1ŸÁ@A›A�1tAœ30Až1•K‚AœAŸ1¤Až 19.869416A 1ŸÁ€A›A¡1dA  _n_u_l_l_A¢1¤A  _n_u_l_l_A£1 ÀAšA¤1Î@A£A¥1dA¤yA¦1Žp€A¤A§1¤A¦tA¨1΀A£A©1dA¨v.yAª1Žp€A¨A«1¤AªtA¬1ŸÁ€A™A­1ŸÁ@A¬A®1ŸÁ@A­A¯1dA®TA°1¦A®0A±1ŸÁ€A­A²1dA± _n_u_l_l_A³1¤A± _n_u_l_l_A´1¤A¬tAµ NN     A¶@D¿;îЊ83/3/@\The angle q between the velocity vector and positive x axis is obtained from tan(Q) = vy/vx.([ \A·- A¸)A¶l255,0,0A¹-Aº)A¶lSymbol255,0,0A·A»-FA¼)A¶l255,0,0A¹A½-A¾)A¶lSymbol255,0,0A»A¿-AÀ)A¶l255,0,0A½AÁ-AÂ)A¶L255,0,0A¿AÃ-AÄ)A¶l255,0,0AÁAÅ-AÆ)A¶L255,0,0AÃAÇ-AÈ)A¶L255,0,0AÅAÇA·*\AÉ-\AÊ+ÿÿÿÿÿÿÿÿÿÿÿÿ"AË- \AÌ-\AÍ!ÿÿÿÿ@NormalArialÿÿÿAÎ3@D(­IQ0-AÏ1 pAÐ1 Á€AÏAÑ1Î@AÐAÒ1dAÑ\QAÓ1Žp€AÑAÔ1¤AÓtAÕ1΀AÐAÖ1dAÕatanA×1Žp€AÕAØ1û€A×AÙ1Î@AØAÚ1dAÙv.yAÛ1Žp€AÙAÜ1¤AÛtAÝ1΀AØAÞ1dAÝv.xAß1Žp€AÝAà1¤AßtAá3@DO:p P0Aâ1 pAã1Á€AâAä1ŸÁ@AãAå1ŸÁ@AäAæ1ŸÁ@AåAç1fAæ 1.047198Aè1•K‚AæAé1¤Aè 1.046127Aê1ŸÁ€AåAë1dAê _n_u_l_l_Aì1¤Aê _n_u_l_l_Aí1΀AäAî1dAí\QAï1Žp€AíAð1¤AïtAñ1ŸÁ€AãAò1ŸÁ@AñAó1ŸÁ@AòAô1dAóTAõ1¦Aó0Aö1ŸÁ€AòA÷1dAö _n_u_l_l_Aø1¤Aö _n_u_l_l_Aù1¤AñtAú9 NN     Aû@Dx‹ ;› x˜ ŒÃÃÃCopyright @Miron Kaufman, 1998(Aü-Aý)Aûn Arial*Aþ-Aÿ+ÿÿÿÿÿÿÿÿÿÿÿÿ"B- B-B!ÿÿÿÿ@NormalArialÿÿÿB@Dß ô ð 7@ùcopyright Miron Kaufman, 1996(B-B)B0,0,128*B-B+ÿÿÿÿÿÿÿÿÿÿÿÿ"B- B -B !ÿÿÿÿ@NormalArialÿÿÿ