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Drop two balls

one in vacuum and one in air

H.Tahsiri

Off[General::spell];
Off[General::spell1];

Clear["Global`*"];

Clear[vequ,initvel,vsol,yequ,inity,ysol,v,y,v0,y0,time,k,yna,vna,t,given,p,g]

vequ=v'[t]==-g+k v[t]^2 
 

vsol=DSolve[{vequ,v[0]==0},v[t],t];

ysol=DSolve[{yequ,y[0]==0},y[t],t];

tsol=Solve[y==y[t],t]

k=3 c roha/(8 R rohw)

given={c->.6,roha->1.2,rohw->10^3,R->1.5 10^(-3),g->9.8,y->-1200}

{c->0.6,roha->1.2,rohw->1000,R->0.0015,g->9.8,y->-1200}

tdown=t/.tsol[[2]]/.given

163.153

impactspeed=y'[t]/.given/.t->tdown

-7.37865

velheightplot=ParametricPlot[Evaluate[{y'[t]  ,y[t]}/.given,{t,0,7},PlotRange->All]];

(* RAIN DROPS IN THE ABCENCE OF AIR ; ARE WE LYING TO OUR STUDENT? YES OR NO  *)

Clear[yna,vna,t]

yna[t_]=-(1/2) g t^2

tna=Sqrt[-2y/g]/.given

15.6492

vna[t_]=D[yna[t],t]

-g t

velheightplotnoair=ParametricPlot[Evaluate[{vna[t]  ,yna[t]}/.given,{t,0,7},PlotRange->All]];

togrther=Show[{velheightplot,velheightplotnoair},PlotRange->{{0,-15},{0,-20}}];

Clear[p,g,t,air,noair]

p[t_]:=p[t]=
Show[Graphics[{
PointSize[.04],Point[{1,y[t]/.given}],
PointSize[.04],Point[{3,yna[t]/.given}]}],
PlotRange->{{0,5},{-40,2}},Axes->Automatic,Ticks->{None,Automatic}];

g=Do[p[t],{t,0,7,.2}]

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