sExact=.5*g*3.5^2
sExact =
   60.0862
sOde45=sValues(end)
sOde45 =
   60.0863
format long
sExact=.5*g*3.5^2
sExact =
  60.086250000000000
sOde45=sValues(end)
sOde45 =
  60.086250000000007
Gallileo(0,[0 30]',0.05)
ans =
  30.000000000000000
   9.283998091603054
[tValues,unknownsValues]=ode45(@(t,unks) Gallileo(t,unks,r),tDesired,unknownsInitialValues)
{Undefined function or variable 'r'.
Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('@(t,unks)Gallileo(t,unks,r)')" style="font-weight:bold">@(t,unks)Gallileo(t,unks,r)</a>

Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('odearguments', 'C:\Program Files\MATLAB\R2018b\toolbox\matlab\funfun\private\odearguments.m', 90)" style="font-weight:bold">odearguments</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2018b\toolbox\matlab\funfun\private\odearguments.m',90,0)">line 90</a>)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.
Error in <a href="matlab:matlab.internal.language.introspective.errorDocCallback('ode45', 'C:\Program Files\MATLAB\R2018b\toolbox\matlab\funfun\ode45.m', 115)" style="font-weight:bold">ode45</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2018b\toolbox\matlab\funfun\ode45.m',115,0)">line 115</a>)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0,
  options, varargin);} 
r=0.2
r =
   0.200000000000000
[tValues,unknownsValues]=ode45(@(t,unks) Gallileo(t,unks,r),tDesired,unknownsInitialValues)
tValues =
                   0
   0.071428571428571
   0.142857142857143
   0.214285714285714
   0.285714285714286
   0.357142857142857
   0.428571428571429
   0.500000000000000
   0.571428571428571
   0.642857142857143
   0.714285714285714
   0.785714285714286
   0.857142857142857
   0.928571428571429
   1.000000000000000
   1.071428571428571
   1.142857142857143
   1.214285714285714
   1.285714285714286
   1.357142857142857
   1.428571428571429
   1.500000000000000
   1.571428571428571
   1.642857142857143
   1.714285714285714
   1.785714285714286
   1.857142857142857
   1.928571428571429
   2.000000000000000
   2.071428571428572
   2.142857142857143
   2.214285714285714
   2.285714285714286
   2.357142857142857
   2.428571428571428
   2.500000000000000
   2.571428571428572
   2.642857142857143
   2.714285714285714
   2.785714285714286
   2.857142857142857
   2.928571428571428
   3.000000000000000
   3.071428571428572
   3.142857142857143
   3.214285714285714
   3.285714285714286
   3.357142857142857
   3.428571428571428
   3.500000000000000
unknownsValues =
                   0                   0
   0.025025479702061   0.700712577602831
   0.100101552806205   1.401414906731393
   0.225227121231892   2.102096739271069
   0.400400354969772   2.802747828466737
   0.625618692224924   3.503357929588811
   0.900878839449648   4.203916800019729
   1.226176771590266   4.904414200169339
   1.601507732161968   5.604839893829435
   2.026866233940558   6.305183649414062
   2.502246059066925   7.005435240174135
   3.027640259153556   7.705584444348730
   3.603041155964383   8.405621046292710
   4.228440341629103   9.105534836765113
   4.903828679715163   9.805315614123433
   5.629196305353159  10.504953184479341
   6.404532625469886  11.204437361919389
   7.229826319856802  11.903757969622889
   8.105065341556095  12.602904840172926
   9.030236918276552  13.301867816704000
  10.005327552505179  14.000636752999039
  11.030323021938361  14.699201513793847
  12.105208380891847  15.397551975848097
  13.229967960914836  16.095678028310381
  14.404585372477197  16.793569573787170
  15.629043505049413  17.491216528396002
  16.903324527822953  18.188608822168547
  18.227409891370687  18.885736400034713
  19.601280328581140  19.582589222273729
  21.024915856517474  20.279157265475458
  22.498295776460580  20.975430522563514
  24.021398675031840  21.671399003312217
  25.594202425960773  22.367052735200595
  27.216684191473853  23.062381763983296
  28.888820424198833  23.757376154517530
  30.610586867177567  24.452025990768796
  32.381958555529046  25.146321376457241
  34.202909818119807  25.840252435735298
  36.073414279592541  26.533809313914539
  37.993444862161155  27.226982178133234
  39.962973785626637  27.919761217361575
  41.981972569667484  28.612136643167130
  44.050412035293675  29.304098690218627
  46.168262307604977  29.995637617156106
  48.335492817369364  30.686743707101016
  50.552072301082212  31.377407267673291
  52.817968803735567  32.067618631796485
  55.133149680839090  32.757368158291534
  57.497581600909534  33.446646232576917
  59.911230546465873  34.135443266952095
sExact
sExact =
  60.086250000000000
sValues40=unknownsValues(:,1)
sValues40 =
                   0
   0.025025479702061
   0.100101552806205
   0.225227121231892
   0.400400354969772
   0.625618692224924
   0.900878839449648
   1.226176771590266
   1.601507732161968
   2.026866233940558
   2.502246059066925
   3.027640259153556
   3.603041155964383
   4.228440341629103
   4.903828679715163
   5.629196305353159
   6.404532625469886
   7.229826319856802
   8.105065341556095
   9.030236918276552
  10.005327552505179
  11.030323021938361
  12.105208380891847
  13.229967960914836
  14.404585372477197
  15.629043505049413
  16.903324527822953
  18.227409891370687
  19.601280328581140
  21.024915856517474
  22.498295776460580
  24.021398675031840
  25.594202425960773
  27.216684191473853
  28.888820424198833
  30.610586867177567
  32.381958555529046
  34.202909818119807
  36.073414279592541
  37.993444862161155
  39.962973785626637
  41.981972569667484
  44.050412035293675
  46.168262307604977
  48.335492817369364
  50.552072301082212
  52.817968803735567
  55.133149680839090
  57.497581600909534
  59.911230546465873
sValues40=unknownsValues(:,1);
r=0.10
r =
   0.100000000000000
[tValues,unknownsValues]=ode45(@(t,unks) Gallileo(t,unks,r),tDesired,unknownsInitialValues);
sValues20=unknownsValues(:,1);
sValues20(end)
ans =
  59.737831761122116
r=0.05
r =
   0.050000000000000
[tValues,unknownsValues]=ode45(@(t,unks) Gallileo(t,unks,r),tDesired,unknownsInitialValues);
sValues10=unknownsValues(:,1);
sValues10(end)
ans =
  59.395794944843324
r=0.025
r =
   0.025000000000000
[tValues,unknownsValues]=ode45(@(t,unks) Gallileo(t,unks,r),tDesired,unknownsInitialValues);
sValues05=unknownsValues(:,1);
sValues06(end)
{Undefined function or variable 'sValues06'.} 
sValues05(end)
ans =
  58.730086344617256
r=0.01
r =
   0.010000000000000
[tValues,unknownsValues]=ode45(@(t,unks) Gallileo(t,unks,r),tDesired,unknownsInitialValues);
sValues02=unknownsValues(:,1);
r=0.005
r =
   0.005000000000000
[tValues,unknownsValues]=ode45(@(t,unks) Gallileo(t,unks,r),tDesired,unknownsInitialValues);
sValues01=unknownsValues(:,1);
sValues02(end)
ans =
  56.867278237908963
sValues01(end)
ans =
  54.140914300876460
tv=tValues
tv =
                   0
   0.071428571428571
   0.142857142857143
   0.214285714285714
   0.285714285714286
   0.357142857142857
   0.428571428571429
   0.500000000000000
   0.571428571428571
   0.642857142857143
   0.714285714285714
   0.785714285714286
   0.857142857142857
   0.928571428571429
   1.000000000000000
   1.071428571428571
   1.142857142857143
   1.214285714285714
   1.285714285714286
   1.357142857142857
   1.428571428571429
   1.500000000000000
   1.571428571428571
   1.642857142857143
   1.714285714285714
   1.785714285714286
   1.857142857142857
   1.928571428571429
   2.000000000000000
   2.071428571428572
   2.142857142857143
   2.214285714285714
   2.285714285714286
   2.357142857142857
   2.428571428571428
   2.500000000000000
   2.571428571428572
   2.642857142857143
   2.714285714285714
   2.785714285714286
   2.857142857142857
   2.928571428571428
   3.000000000000000
   3.071428571428572
   3.142857142857143
   3.214285714285714
   3.285714285714286
   3.357142857142857
   3.428571428571428
   3.500000000000000
plot(tv,sValues40,tv,sValues20,tv,sValues10,tv,sValues05,tv,sValues02.tv,sValues01)
{Dot indexing is not supported for variables of this type.} 
plot(tv,sValues40,tv,sValues20,tv,sValues10,tv,sValues05,tv,sValues02,tv,sValues01)