{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":2,"images":2,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Sheet1","index":0,"n_rows":1024,"n_cols":18,"rows_kept":1024,"cut":false,"hidden":false,"merged":[[12,13,14,15],[12,6,12,8],[14,2,14,4],[18,2,19,4],[12,0,12,1],[12,2,12,3],[12,4,12,5]]}
["Projectile motion with Air Resistance"]
[]
["Instructions: ",null,"Set values in yellow boxes"]
[null,null,"Avoid u=0 (try .001 instead)"]
[null,null,"Avoid ɵ=90 (try 89.99 instead)"]
[null,null,"Use slider beside graphs to set air resistance"]
[null,null,"Use a small time increment (around 0.005)"]
[null,null,null,"If RHS of graph is truncated, increase time increment"]
[null,null,null,"If graph is too compressed on x-axis, decrease time increment"]
[]
[]
[]
["aair=k.A.v2/m",null,"let k.A/m=",null,{"$f":"O16/1000","v":3.1E-2},null,"don't touch, set with slider",null,null,null,null,null,null,"don't touch, intermediate values"]
["u",18]
["ɵ to horz",{"$f":"P16","v":56},"don't touch, set with slider"]
["av",-9.8000000000000007,null,null,null,null,null,null,null,null,null,null,null,{"$f":"B15*PI()/180","v":0.97738438111682457},31,56]
["sv:launch",0]
["sv:land",0]
["uh",{"$f":"$B$14*COS($N$16)","v":10.065472262473442},"don't touch, automatically calculated"]
["uv",{"$f":"$B$14*SIN($N$16)","v":14.922676305990752}]
["time inc"]
[5.0000000000000001E-3]
["time","sno air resist:x","sno air resist:xy","sno air resist:t:trn","truncate","aair","aair:x","aair:y","vair resist:x","vair resist:y","ɵ to horz","vair resist","sair resist:x","sair resist:y","sair resist:y:trn","truncate",null,"Set air resistance"]
[0,{"$f":"IF(E24=0,B23,$B$19*A24)","v":0},{"$f":"$B$20*A24+0.5*$B$20*A24^2+$B$17","v":0},{"$f":"IF(E24=1,C24,$B$18)","v":0},{"$f":"IF(AND(C25-C24<0,C24<$B$18),0,1)","v":1},null,null,null,{"$f":"B19","v":10.065472262473442},{"$f":"B20","v":14.922676305990752},{"$f":"180/PI()*ATAN(J24/I24)","v":56.000000000000007},{"$f":"SQRT(I24^2+J24^2)","v":18},0,{"$f":"$B$17","v":0},{"$f":"IF(P24=1,N24,$B$18)","v":0},{"$f":"IF(AND(N25-N24<0,N24<$B$18),0,1)","v":1},null,"none"]
[{"$f":"A24+$A$22","v":5.0000000000000001E-3},5.032736131236721E-2,{"$f":"$B$20*A25+0.5*$B$16*A25^2+$B$17","v":7.449088152995377E-2},{"$f":"IF(E25=1,C25,$B$18)","v":7.449088152995377E-2},{"$f":"IF(AND(C26-C25<0,C25<$B$18),0,1)","v":1},{"$f":"-$E$13*L24^2","v":-10.044},{"$f":"$F25*COS(PI()/180*$K24)","v":-5.6165335224601796},{"$f":"$F25*SIN(PI()/180*$K24)","v":-8.3268533787428396},{"$f":"I24+G25*$A$22","v":10.037389594861141},{"$f":"J24+(H25+$B$16)*$A$22","v":14.832042039097038},{"$f":"180/PI()*ATAN(J25/I25)","v":55.912339311508291},{"$f":"SQRT(I25^2+J25^2)","v":17.909178119851525},{"$f":"IF(P25=0,M24,M24+I25*$A$22)","v":5.0186947974305708E-2},{"$f":"N24+J25*$A$22","v":7.4160210195485188E-2},{"$f":"IF(P25=1,N25,$B$18)","v":7.4160210195485188E-2},1]
[{"$f":"A25+$A$22","v":0.01},0.10065472262473442,0.14873676305990755,0.14873676305990755,1,-9.9428984887856267,{"$f":"$F26*COS(PI()/180*$K25)","v":-5.5726033414940881},{"$f":"$F26*SIN(PI()/180*$K25)","v":-8.2345201655387559},{"$f":"I25+G26*$A$22","v":10.00952657815367},14.741869438269344,{"$f":"180/PI()*ATAN(J26/I26)","v":55.824034773286982},{"$f":"SQRT(I26^2+J26^2)","v":17.818903918416094},{"$f":"IF(P26=0,M25,M25+I26*$A$22)","v":0.10023458086507406},0.14786955738683191,0.14786955738683191,1]
[1.4999999999999999E-2,0.15098208393710164,0.22273764458986126,0.22273764458986126,1,-9.8429134424660774,-5.5291225633135266,-8.1432026080490374,9.981880965337103,14.652153425229098,55.735081285885066,17.729172219892611,0.15014398569175957,0.2211303245129774,0.2211303245129774,1]
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[2.5000000000000001E-2,0.25163680656183607,0.37000440764976877,0.37000440764976877,1,-9.6462334596512971,-5.4434849218975572,-7.9635602504891096,9.9272331152871107,14.474071188499085,55.555206813172703,17.551316021740146,0.24955240396767811,0.3663151254042305,0.3663151254042305,1]
[3.0000000000000002E-2,0.30196416787420327,0.44327028917972255,0.44327028917972255,1,-9.549509516944763,-5.4013161744645286,-7.8752089240658538,9.9002265344147879,14.385695143878756,55.464275375045226,17.463181560223997,0.29905353663975204,0.43824360112362426,0.43824360112362426,1]
[3.5000000000000003E-2,0.35229152918657047,0.51629117070967634,0.51629117070967634,1,-9.4538440163657711,-5.3595730571928124,-7.7878201911952099,9.873428669128824,14.29775604292278,55.372674081198468,17.375569675475674,0.34842067998539616,0.50973238133823817,0.50973238133823817,1]
[0.04,0.40261889049893768,0.58906705223963018,0.58906705223963018,1,-9.3592230679666031,-5.3182498810648937,-7.7013813461295006,9.8468374197234994,14.210249136192132,55.280397575552932,17.288475574298509,0.39765486708401365,0.58078362701919883,0.58078362701919883,1]
[4.4999999999999998E-2,0.45294625181130488,0.66159793376958387,0.66159793376958387,1,-9.2656330181766027,-5.2773410546643271,-7.6158798979683811,9.8204507144501783,14.123169736702291,55.187440449342823,17.201894536551734,0.44675712065626455,0.65139947570271028,0.65139947570271028,1,null,"lots"]
[4.9999999999999996E-2,0.50327361312367203,0.7338838152995375,0.7338838152995375,1,-9.1730604450460991,-5.2368410822326572,-7.5313035663097283,9.7942665090390157,14.036513218870743,55.093797240660429,17.115821914054155,0.49572845320145964,0.72158204179706398,0.72158204179706398,1]
[5.4999999999999993E-2,0.55360097443603928,0.8059246968294913,0.8059246968294913,1,-9.0814921536021096,-5.1967445617723964,-7.4476402770022201,9.768282786230154,13.950275017485732,54.999462433999739,17.030253129511813,0.54456986713261046,0.79133341688449266,0.79133341688449266,1,null,"Set air launch angle"]
[5.9999999999999991E-2,0.60392833574840643,0.87772057835944495,0.87772057835944495,1,-8.9909151713126541,-5.1570461831947272,-7.3648781579966922,9.7424975553141806,13.864450626695747,54.904430459799713,16.94518367546917,0.59328235490918135,0.86065567001797139,0.86065567001797139,1]
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[7.4999999999999997E-2,0.75491041968550809,1.0916382229493065,1.0916382229493065,1,-8.7250055983596653,-5.0402881388133789,-7.1218830493869154,9.66631329568723,13.609416129127418,54.615095015927459,16.692927247973412,0.73865603932793222,1.0660680563805767,1.0660680563805767,1]
[0.08,0.80523778099787535,1.1624541044792602,1.1624541044792602,1,-8.6382684232901283,-5.002131002631776,-7.0426107932585174,9.6413026406740716,13.525203075161125,54.517217578858734,16.609811402704629,0.78686255253130255,1.1336940717563824,1.1336940717563824,1]
[8.5000000000000006E-2,0.85556514231024261,1.233024986009214,1.233024986009214,1,-8.5524608798359179,-4.9643467746778267,-6.9641832401129147,9.6164809068006818,13.441382158960559,54.418614299620813,16.527173363103724,0.83494495706530591,1.2009009825511852,1.2009009825511852,1]
[9.0000000000000011E-2,0.90589250362260987,1.3033508675391678,1.3033508675391678,1,-8.4675712405966426,-4.9269306597798233,-6.8865896486069875,9.5918462535017834,13.357949210717525,54.319279274725588,16.445009019970929,0.88290418833281481,1.2676907286047727,1.2676907286047727,1]
[9.5000000000000015E-2,0.95621986493497713,1.3734317490691217,1.3734317490691217,1,-8.3835879716746824,-4.8898779428673471,-6.8098194530154625,9.5673968637874474,13.274900113452448,54.219206543434368,16.363314327218362,0.93074117265175205,1.334065229172035,1.334065229172035,1]
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[0.12500000000000003,1.2581840328091805,1.7887720382488443,1.7887720382488443,1,-7.8980996872262574,-4.6749386686530094,-6.3659191884358961,9.4244921823939833,12.784442292506585,53.602937192389064,15.882789982444404,1.2152466505551076,1.7236970265424483,1.7236970265424483,1,null,{"$f":"MAX(B23:B1023)","v":30.649363039231201}]
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[0.20000000000000009,2.0130944524946894,2.7885352611981515,2.7885352611981515,1,-6.8107546963907293,-4.1881409276359411,-5.3708337439050498,9.0937685679331981,11.612765907072239,51.936080456936651,14.749676565253528,1.9086286045432201,2.635201394571582,2.635201394571582,1]
[0.2050000000000001,2.0634218138070564,2.8532261427281056,2.8532261427281056,1,-6.7441417221672628,-4.1580344992247875,-5.309820775876875,9.0729783954370742,11.537216803192855,51.818148623706627,14.677408099795532,1.9539934965204055,2.6928874785875463,2.6928874785875463,1]
[0.2100000000000001,2.1137491751194237,2.9176720242580592,2.9176720242580592,1,-6.6782155643662477,-4.1282020043041978,-5.2494296200446779,9.0523373854155533,11.461969655092632,51.699325174566454,14.605531846312767,1.9992551834474832,2.7501973268630096,2.7501973268630096,1]
[0.21500000000000011,2.1640765364317911,2.9818729057880131,2.9818729057880131,1,-6.6129683759233489,-4.0986402609538901,-5.189653047386706,9.031844184110783,11.387021389855699,51.579602645508217,14.534045049437786,2.044414404368037,2.8071324338122881,2.8071324338122881,1]
[0.22000000000000011,2.2144038977441585,3.045828787317967,3.045828787317967,1,-6.5483924304716981,-4.0693461377924329,-5.1304839376313067,9.0114974534218213,11.312368970167542,51.458973505059902,14.46294499990363,2.0894718916351462,2.8636942786631256,2.8636942786631256,1]
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