ab Trig Formulas on an iPad - Drop Straight Down

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2017-10-08 03:55

In collections Math Year 4 Unit 1

This example demonstrates on an iPad using GeoGebra the dynamic graphical phenomenon of an object dropping straight down, involving trigonometric functions and integral calculations. Core mathematical concepts include vectors, trigonometry, integral calculus, and optimization problems. Key GeoGebra commands and objects used in the construction are Intersect, AttachCopyToView, r, hcfw, trev, hzcrto, wtr, ratecrt, Hcfw2wtr, Rateang, Haddon, Htotal, T2fall, Hzdvr, f, A, stroke1. Suitable for high school and above mathematics learning, illustrating the application of integral, vector, and trigonometric functions in physical phenomena.

GeoGebra Commands & Parameters

Intersect(Hzdvr, f, (9.81094355745193, -8.463856136758254)) → A
AttachCopyToView(PolyLine[(-8.00740462480568, -15.4988689005249), (NaN, NaN), (-8.00740462480568, -15.4988689005249), (-7.05718830814641, -15.18994967691), (-6.10697199148714, -15.18994967691), (-4.998386288718, -15.18994967691), (-4.04816997205873, -15.0354900651026), (-3.25632304150934, -14.7265708414877), (-2.78121488317971, -14.4176516178728), (-2.30610672485007, -13.9542727824505), (-2.14773733874019, -13.4908939470282), (-2.30610672485007, -12.4096766643761), (-2.62284549706983, -11.9462978289537), (-3.41469242761922, -11.328459381724), (-4.20653935816861, -11.328459381724), (-4.84001690260812, -11.9462978289537), (-4.84001690260812, -12.718595887991), (-4.68164751649824, -13.1819747234133), (-4.52327813038836, -13.6453535588356), (-4.36490874427848, -14.1087323942579), (-4.04816997205873, -14.5721112296803), (-3.88980058594885, -15.18994967691), (-3.73143119983897, -15.8077881241398), (-3.41469242761922, -16.7345457949845), (-3.25632304150934, -17.1979246304068), (-3.09795365539946, -17.8157630776366), (-3.09795365539946, -18.4336015248663), (-2.93958426928958, -19.0514399720961), (-2.93958426928958, -19.8237380311333), (-2.93958426928958, -20.4415764783631), (-3.09795365539946, -21.0594149255929), (-3.5730618137291, -21.5227937610152), (-4.36490874427848, -21.9861725964375), (-4.998386288718, -22.140632208245), (-5.63186383315751, -22.140632208245), (-6.26534137759702, -21.9861725964375), (-6.74044953592666, -21.6772533728226), (-7.05718830814641, -20.9049553137854), (-7.21555769425629, -20.4415764783631), (-7.05718830814641, -19.9781976429408), (-6.58208014981678, -19.6692784193259), (-5.31512506093775, -19.9781976429408), (-4.84001690260812, -20.1326572547482), (-4.20653935816861, -20.4415764783631), (-3.73143119983897, -20.750495701978), (-3.09795365539946, -21.0594149255929), (-2.46447611095995, -21.2138745374003), (-1.98936795263031, -21.3683341492078), (-1.19752102208092, -21.5227937610152), (-0.564043477641411, -21.6772533728226), (0.386172839017858, -21.6772533728226), (0.861280997347492, -21.0594149255929), (0.861280997347492, -20.1326572547482), (0.861280997347492, -19.2058995839036), (0.702911611237616, -18.7425207484812), (0.544542225127737, -18.2791419130589), (0.544542225127737, -18.8969803602887), (0.861280997347492, -19.6692784193259), (1.33638915567713, -20.5960360901705), (1.96986670011664, -21.0594149255929), (2.76171363066603, -21.2138745374003), (3.55356056121542, -21.0594149255929), (4.02866871954506, -20.4415764783631), (4.18703810565493, -19.6692784193259), (4.66214626398457, -19.2058995839036), (5.1372544223142, -19.360359195711), (5.45399319453396, -19.8237380311333), (5.77073196675372, -20.2871168665557), (6.24584012508335, -20.9049553137854), (6.72094828341298, -20.750495701978), (6.72094828341298, -19.9781976429408), (6.87931766952286, -19.5148188075184), (7.19605644174262, -19.0514399720961), (7.82953398618213, -19.360359195711), (8.14627275840188, -19.8237380311333), (8.46301153062164, -20.4415764783631), (8.93811968895127, -21.0594149255929), (9.57159723339079, -21.2138745374003), (10.0467053917204, -21.0594149255929), (10.3634441639402, -20.4415764783631), (10.5218135500501, -19.9781976429408), (10.6801829361599, -19.5148188075184), (10.8385523222698, -19.0514399720961), (11.3136604805994, -18.7425207484812), (10.6801829361599, -19.2058995839036), (10.6801829361599, -19.9781976429408), (11.3136604805994, -20.750495701978), (11.7887686389291, -21.0594149255929), (12.4222461833686, -21.3683341492078), (13.0557237278081, -21.5227937610152), (13.5308318861377, -21.6772533728226), (14.0059400444674, -21.2138745374003), (14.0059400444674, -20.5960360901705), (13.8475706583575, -19.8237380311333), (13.3724625000279, -18.8969803602887), (12.8973543416982, -17.970222689444), (12.1055074111488, -16.8890054067919), (11.3136604805994, -16.1167073477547), (10.8385523222698, -15.3444092887175), (10.3634441639402, -14.8810304532952), (10.2050747778303, -15.3444092887175), (10.3634441639402, -15.9622477359473), (10.6801829361599, -16.580086183177), (10.9969217083797, -17.3523842422142), (11.4720298667093, -17.8157630776366), (11.947138025039, -18.4336015248663), (12.4222461833686, -19.0514399720961), (12.7389849555883, -19.5148188075184), (13.214093113918, -19.9781976429408), (13.8475706583575, -20.750495701978), (14.481048202797, -20.750495701978), (14.7977869750168, -20.2871168665557), (15.1145257472365, -19.5148188075184), (15.2728951333464, -18.8969803602887), (15.2728951333464, -18.2791419130589), (15.4312645194562, -18.7425207484812), (15.5896339055661, -19.360359195711), (16.0647420638958, -19.9781976429408), (16.3814808361155, -20.5960360901705), (17.014958380555, -21.0594149255929), (17.4900665388847, -21.2138745374003), (17.9651746972143, -21.3683341492078), (18.7570216277637, -21.2138745374003), (19.0737603999834, -20.5960360901705), (19.2321297860933, -20.1326572547482), (19.0737603999834, -19.2058995839036), (18.5986522416538, -18.5880611366738), (18.4402828555439, -19.360359195711), (18.5986522416538, -20.1326572547482), (19.0737603999834, -21.0594149255929), (19.8656073305328, -22.6040110436673), (20.3407154888625, -23.530768714512), (20.8158236471921, -24.6119859971641), (21.1325624194118, -25.3842840562013), (21.1325624194118, -26.1565821152385), (20.1823461027526, -25.5387436680087), (19.7072379444229, -25.0753648325864), (19.5488685583131, -24.6119859971641), (19.3904991722032, -23.8396879381268), (19.5488685583131, -23.0673898790896), (20.4990848749723, -23.0673898790896), (21.1325624194118, -23.0673898790896), (NaN, NaN), (1.81149731400676, -16.1167073477547), (NaN, NaN), (1.81149731400676, -16.1167073477547), true], 1, (-9.716456293234058, -25.54028325569991), (35.50557673188053, 62.15668388788925), (0, 693), (555, 0)) → stroke1

AI Drawing Prompt Reference

Draw a dynamic graph showing an object dropping straight down, involving trigonometric functions and integral calculations. The graph features a curved path representing the object's trajectory and a vertical line segment indicating the direction of descent. The path starts from the upper left, reaches a peak, and then descends gradually to the lower right. The entire graph is set against a coordinate system with clear axis labels, and the curve and line segment are highlighted in color, illustrating the application of vectors, trigonometric functions, and integrals in physical phenomena.

The prompt above was compiled from the original drawing commands and is for reference only.