Expression 24: "S" Subscript, "b" , Baseline left parenthesis, "x" , "y" , right parenthesis equals signum left parenthesis, sin left parenthesis, arctan left parenthesis, "y" minus "P" Subscript, 3 , Baseline . "y" , "x" minus "P" Subscript, 3 , Baseline . "x" , right parenthesis minus "A" Subscript, 2 , Baseline , right parenthesis , right parenthesisSbx,y=signsinarctany−P3.y,x−P3.x−A2
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Expression 25: "S" Subscript, "b" "e" "t" "w" "B" , Baseline left parenthesis, "x" , "y" , right parenthesis equals left brace, 0 less than left parenthesis, "x" minus "P" Subscript, 3 , Baseline . "x" , right parenthesis cos left parenthesis, "A" Subscript, 2 , Baseline , right parenthesis plus left parenthesis, "y" minus "P" Subscript, 3 , Baseline . "y" , right parenthesis sin left parenthesis, "A" Subscript, 2 , Baseline , right parenthesis , right brace left brace, 1 greater than left parenthesis, "x" minus "P" Subscript, 3 , Baseline . "x" , right parenthesis cos left parenthesis, "A" Subscript, 2 , Baseline , right parenthesis plus left parenthesis, "y" minus "P" Subscript, 3 , Baseline . "y" , right parenthesis sin left parenthesis, "A" Subscript, 2 , Baseline , right parenthesis , right braceSbetwBx,y=0<x−P3.xcosA2+y−P3.ysinA21>x−P3.xcosA2+y−P3.ysinA2
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Expression 26: "S" Subscript, "b" "e" "t" "w" "O" , Baseline left parenthesis, "x" , "y" , right parenthesis equals left brace, 0 less than left parenthesis, "x" minus "P" Subscript, 1 , Baseline . "x" , right parenthesis cos left parenthesis, "A" Subscript, 1 , Baseline , right parenthesis plus left parenthesis, "y" minus "P" Subscript, 1 , Baseline . "y" , right parenthesis sin left parenthesis, "A" Subscript, 1 , Baseline , right parenthesis : 1 , 0 , right brace left brace, 1 greater than left parenthesis, "x" minus "P" Subscript, 1 , Baseline . "x" , right parenthesis cos left parenthesis, "A" Subscript, 1 , Baseline , right parenthesis plus left parenthesis, "y" minus "P" Subscript, 1 , Baseline . "y" , right parenthesis sin left parenthesis, "A" Subscript, 1 , Baseline , right parenthesis : 1 , 0 , right braceSbetwOx,y=0<x−P1.xcosA1+y−P1.ysinA1:1,01>x−P1.xcosA1+y−P1.ysinA1:1,0
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Expression 27: "r" equals 0.1r=0.1
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Expression 28: "S" Subscript, "b" "e" "t" "w" "O" , Baseline left parenthesis, "p" . "x" , "p" . "y" , right parenthesisSbetwOp.x,p.y
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Expression 29: "P" Subscript, "O" "B" , Baseline left parenthesis, "x" , "y" , right parenthesis equals left parenthesis, left parenthesis, "x" minus "P" Subscript, 1 , Baseline . "x" , right parenthesis cos left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis plus left parenthesis, "y" minus "P" Subscript, 1 , Baseline . "y" , right parenthesis sin left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis plus "P" Subscript, 3 , Baseline . "x" , negative left parenthesis, "x" minus "P" Subscript, 1 , Baseline . "x" , right parenthesis sin left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis plus left parenthesis, "y" minus "P" Subscript, 1 , Baseline . "y" , right parenthesis cos left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis plus "P" Subscript, 3 , Baseline . "y" , right parenthesisPOBx,y=x−P1.xcosA1−A2+y−P1.ysinA1−A2+P3.x,−x−P1.xsinA1−A2+y−P1.ycosA1−A2+P3.y
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Expression 30: "P" Subscript, "B" "O" , Baseline left parenthesis, "x" , "y" , right parenthesis equals left parenthesis, left parenthesis, "x" minus "P" Subscript, 3 , Baseline . "x" , right parenthesis cos left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis plus left parenthesis, "y" minus "P" Subscript, 3 , Baseline . "y" , right parenthesis sin left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis plus "P" Subscript, 1 , Baseline . "x" , left parenthesis, "y" minus "P" Subscript, 3 , Baseline . "y" , right parenthesis cos left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis minus left parenthesis, "x" minus "P" Subscript, 3 , Baseline . "x" , right parenthesis sin left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis plus "P" Subscript, 1 , Baseline . "y" , right parenthesisPBOx,y=x−P3.xcosA2−A1+y−P3.ysinA2−A1+P1.x,y−P3.ycosA2−A1−x−P3.xsinA2−A1+P1.y
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Expression 31: "V" Subscript, "O" "B" , Baseline left parenthesis, "x" , "y" , right parenthesis equals left parenthesis, "v" . "x" cos left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis plus "v" . "y" sin left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis , negative "v" . "x" sin left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis plus "v" . "y" cos left parenthesis, "A" Subscript, 2 , Baseline minus "A" Subscript, 1 , Baseline , right parenthesis , right parenthesisVOBx,y=v.xcosA2−A1+v.ysinA2−A1,−v.xsinA2−A1+v.ycosA2−A1
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Expression 32: "V" Subscript, "B" "O" , Baseline left parenthesis, "x" , "y" , right parenthesis equals left parenthesis, "v" . "x" cos left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis plus "v" . "y" sin left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis , "v" . "y" cos left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis minus "v" . "x" sin left parenthesis, "A" Subscript, 1 , Baseline minus "A" Subscript, 2 , Baseline , right parenthesis , right parenthesisVBOx,y=v.xcosA1−A2+v.ysinA1−A2,v.ycosA1−A2−v.xsinA1−A2
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Expression 33: "d" Subscript, "x" , Baseline equals 18dx=18
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Expression 34: "p" Subscript, "a" , Baseline equals left brace, "S" Subscript, "b" "e" "t" "w" "O" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis equals 1 : left brace, "S" Subscript, "O" , Baseline left parenthesis, "p" . "x" , "p" . "y" , right parenthesis equals negative "S" Subscript, "O" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis : "p" Subscript, "a" 1 , Baseline , "S" Subscript, "b" "e" "t" "w" "B" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis equals 1 : left brace, "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" , "p" . "y" , right parenthesis equals negative "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis : "p" Subscript, "a" 2 , Baseline , "p" Subscript, "a" 3 , Baseline , right brace , "p" Subscript, "a" 3 , Baseline , right brace , "S" Subscript, "b" "e" "t" "w" "B" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis equals 1 : left brace, "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" , "p" . "y" , right parenthesis equals negative "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis : "p" Subscript, "a" 2 , Baseline , "p" Subscript, "a" 3 , Baseline , right brace , "p" Subscript, "a" 3 , Baseline , right bracepa=SbetwOp.x+v.xdx1000,p.y+v.ydx1000=1:SOp.x,p.y=−SOp.x+v.xdx1000,p.y+v.ydx1000:pa1,SbetwBp.x+v.xdx1000,p.y+v.ydx1000=1:Sbp.x,p.y=−Sbp.x+v.xdx1000,p.y+v.ydx1000:pa2,pa3,pa3,SbetwBp.x+v.xdx1000,p.y+v.ydx1000=1:Sbp.x,p.y=−Sbp.x+v.xdx1000,p.y+v.ydx1000:pa2,pa3,pa3
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Expression 35: "v" Subscript, "a" , Baseline equals left brace, "S" Subscript, "b" "e" "t" "w" "O" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis equals 1 : left brace, "S" Subscript, "O" , Baseline left parenthesis, "p" . "x" , "p" . "y" , right parenthesis equals negative "S" Subscript, "O" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis : "v" Subscript, "a" 2 , Baseline , "S" Subscript, "b" "e" "t" "w" "B" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis equals 1 : left brace, "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" , "p" . "y" , right parenthesis equals negative "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis : "v" Subscript, "a" 1 , Baseline , "v" Subscript, "a" 3 , Baseline , right brace , "v" Subscript, "a" 3 , Baseline , right brace , "S" Subscript, "b" "e" "t" "w" "B" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis equals 1 : left brace, "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" , "p" . "y" , right parenthesis equals negative "S" Subscript, "b" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesis : "v" Subscript, "a" 1 , Baseline , "v" Subscript, "a" 3 , Baseline , right brace , "v" Subscript, "a" 3 , Baseline , right braceva=SbetwOp.x+v.xdx1000,p.y+v.ydx1000=1:SOp.x,p.y=−SOp.x+v.xdx1000,p.y+v.ydx1000:va2,SbetwBp.x+v.xdx1000,p.y+v.ydx1000=1:Sbp.x,p.y=−Sbp.x+v.xdx1000,p.y+v.ydx1000:va1,va3,va3,SbetwBp.x+v.xdx1000,p.y+v.ydx1000=1:Sbp.x,p.y=−Sbp.x+v.xdx1000,p.y+v.ydx1000:va1,va3,va3
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Expression 36: "g" equals left parenthesis, 0 , negative 9.8 , right parenthesisg=0,−9.8
Expression 39: "a" Subscript, 1 , Baseline equals "p" Subscript, "t" "e" "m" "p" , Baseline to "p" Subscript, "a" , Baselinea1=ptemp→pa
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Expression 40: "a" Subscript, 2 , Baseline equals "v" to "v" Subscript, "a" , Baselinea2=v→va
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Expression 41: "a" Subscript, 3 , Baseline equals "p" to "p" Subscript, "t" "e" "m" "p" , Baselinea3=p→ptemp
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Expression 42: "v" Subscript, "a" 1 , Baseline equals "V" Subscript, "O" "B" , Baseline left parenthesis, "v" . "x" plus "g" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "v" . "y" plus "g" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesisva1=VOBv.x+g.xdx1000,v.y+g.ydx1000
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Expression 43: "v" Subscript, "a" 2 , Baseline equals "V" Subscript, "B" "O" , Baseline left parenthesis, "v" . "x" plus "g" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "v" . "y" plus "g" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesisva2=VBOv.x+g.xdx1000,v.y+g.ydx1000
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Expression 44: "v" Subscript, "a" 3 , Baseline equals left parenthesis, "v" . "x" plus "g" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "v" . "y" plus "g" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesisva3=v.x+g.xdx1000,v.y+g.ydx1000
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Expression 45: "p" Subscript, "a" 1 , Baseline equals "P" Subscript, "O" "B" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesispa1=POBp.x+v.xdx1000,p.y+v.ydx1000
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Expression 46: "p" Subscript, "a" 2 , Baseline equals "P" Subscript, "B" "O" , Baseline left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesispa2=PBOp.x+v.xdx1000,p.y+v.ydx1000
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Expression 47: "p" Subscript, "a" 3 , Baseline equals left parenthesis, "p" . "x" plus "v" . "x" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , "p" . "y" plus "v" . "y" StartFraction, "d" Subscript, "x" , Baseline Over 1000 , EndFraction , right parenthesispa3=p.x+v.xdx1000,p.y+v.ydx1000