Clear[y,t,given,v0,g,y0]
given1={v0->50,g->9.8,y0->0} {v0 -> 50, g -> 9.8, y0 -> 0}
y=y0+v0 t-.5 g t^2 2 -0.5 g t + t v0 + y0
ynoair = y/.given1 2 50 t - 4.9 t
totaltnoair=Solve[ynoair==0,t] {{t -> 0.}, {t -> 10.2041}}
yupdownoairplot=Plot[ynoair,{t,0,10.2041}];
Clear[y,v]
given2={b->.1,g->9.8,v0->50} {b -> 0.1, g -> 9.8, v0 -> 50}
aupair=-g -b v[t] -g - b v[t]
vupair=DSolve[{v'[t]==aupair,v[0]==v0},v[t],t] b t g - E g + b v0 {{v[t] -> -----------------}} b t b E
vupairsymbl=vupair[[1,1,2]] b t g - E g + b v0 ----------------- b t b E
vupairnum=vupairsymbl/.given2 0.1 t 10. (14.8 - 9.8 E ) ----------------------- 0.1 t E
tupair=Solve[vupairnum==0,t] {{t -> 4.12245}}
tupairvalue=tupair[[1,1,2]] 4.12245
yupair=DSolve[{y'[t]==vupairsymbl,y[0]==0},y[t],t] b t b t b t -g + E g - b E g t - b v0 + b E v0 {{y[t] -> -------------------------------------------}} 2 b t b E
yupairsymbl=yupair[[1,1,2]] b t b t b t -g + E g - b E g t - b v0 + b E v0 ------------------------------------------- 2 b t b E
tocheck=Limit[yupairsymbl,b->0] 2 -(g t ) ------- + t v0 2
yupairnum=yupairsymbl/.given2 0.1 t 0.1 t 100. (-14.8 + 14.8 E - 0.98 E t) ------------------------------------------ 0.1 t E
yupvalue=yupairnum/.t->tupairvalue 96.0001
yupairtable=Table[{t,yupairnum},{t,0,tupairvalue,.09}];
yupairplot=ListPlot[yupairtable,PlotJoined->True];
Clear[v,t,y]
given3={b->.1,g->9.8,v0->50} {b -> 0.1, g -> 9.8, v0 -> 50}
adownair=g-b v[t] g - b v[t]
vdownair=DSolve[{v'[t]==adownair,v[0]==0},v[t],t] g g {{v[t] -> - - ------}} b b t b E
vdownairsymbl=vdownair[[1,1,2]] g g - - ------ b b t b E
vdownairnum=vdownairsymbl/.given3 98. 98. - ------ 0.1 t E
ydownair=DSolve[{y'[t]==vdownairsymbl,y[0]==0},y[t],t] g g g t {{y[t] -> -(--) + ------- + ---}} 2 2 b t b b b E
ydownairsymbl=ydownair[[1,1,2]] g g g t -(--) + ------- + --- 2 2 b t b b b E
ydownairnum=ydownairsymbl/.given3 980. -980. + ------ + 98. t 0.1 t E
tdownair=FindRoot[ydownairnum==96.0001,{t,4}] {t -> 4.77834}
tdownairvalue=tdownair[[1,2]] 4.77834
tupairvalue 4.12245
ydownairtable=Table[{t+tupairvalue,96.0001-ydownairnum}, {t,0,tdownairvalue,.09}];
ydownairplot=ListPlot[ydownairtable,PlotJoined->True, AxesOrigin->{tupairvalue,0}];
yupdownairtable=Join[yupairtable,ydownairtable];
yupdownairplot=ListPlot[yupdownairtable,PlotJoined->True];
together=Show[{yupdownairplot,yupdownoairplot}];
ynoair 2 50 t - 4.9 t
g=Table[{0,ynoair},{t,0,10.2,.1}];
Length[g] 103
gg=Table[{t,ynoair},{t,0,10.2,.1}];
gair=Table[{0,yupdownairtable[[i,2]]},{i,1,100}];
ggair=Table[yupdownairtable[[i]],{i,1,100}];
Length[gair] 100
Length[ggair] 100
Do[ Show[(*(Graphics[Dashing[{.008}],Thickness[.003],Line[{g[[n]],gg[[n]]}]])*) ListPlot[gg,PlotJoined->True,PlotRange->{{0,10.20},{0,150}}, PlotStyle->{Thickness[.01],RGBColor[0,1,0]},DisplayFunction->Identity], ListPlot[{gg[[3n]]},PlotRange->{{0,10.20},{0,150}}, PlotStyle->{RGBColor[1,0,0],PointSize[.02]}, DisplayFunction->Identity], ListPlot[{g[[3n]]},PlotRange->{{0,10.20},{0,150}}, PlotStyle->{RGBColor[1,0,1],PointSize[.05]}, DisplayFunction->Identity], ListPlot[ggair,PlotJoined->True,PlotRange->{{0,10.20},{0,150}}, PlotStyle->{Thickness[.01],RGBColor[0,1,0]},DisplayFunction->Identity], ListPlot[{ggair[[3n]]},PlotRange->{{0,10.20},{0,150}}, PlotStyle->{RGBColor[1,0,0],PointSize[.02]}, DisplayFunction->Identity], ListPlot[{gair[[3n]]},PlotRange->{{0,10.20},{0,150}}, PlotStyle->{RGBColor[1,0,1],PointSize[.05]}, DisplayFunction->Identity], DisplayFunction->$DisplayFunction], (* end Show *) {n,1,33}] (* end Do *) Back to Problems