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1) In the following code, I want to AnimateAnimate just the Elapsed Time (tt) variable. How do I write an AnimateAnimate inside the ManipulateManipulate?

2) How do I have the graph not show until the Animationanimation? I want the red line to advance along with the ball, not just have the ball follow the red line's already shown path. f[t_, v_, a_] :=v*Cos[a Degree]*t (the x value at time t) g[t_, v_, a_] :=v*Sin[a Degree]*t - (9.82*t^2)/2 (the y value at time t) c[t_, v_, a_] := {f[t, v, a],Max[g[t, v, a], 0]} (the x and y value at time t) xmax[v_, a_] := (v^2*Sin[2*a])/9.8 (x value when ball hits ground) ymax[v_, a_] := (v^2*(Sin^2)[a])/19.6 (maximum height) tmax[v_, a_] := (v*Sin[a Degree]/4.9) (time when ball hits ground)

f[t_, v_, a_] :=v*Cos[a Manipulate[Degree]*t        (*the x value at time t*)
g[t_, v_, a_] :=v*Sin[a Degree]*t Show[- (9.82*t^2)/2 (*the y value at time t*)
c[t_, v_, a_] := {f[t, v, a],Max[g[t, v, a], 0]} ParametricPlot[(*the x and y value at time t*)
xmax[v_, a_] := (v^2*Sin[2*a])/9.8   (*x value when ball hits ground*)
ymax[v_, a_] := (v^2*(Sin^2)[a])/19.6   (*maximum height*)
tmax[v_, a_] := (v*Sin[a Degree]/4.9)  (*time when ball hits ground*)

Manipulate[
Show[
ParametricPlot[
{f[t, v, a], Max[g[t, v, a], 0]}, {t, 0, 20},
PlotStyle -> {Thick, Red}
],          (*close parametric plot*)
ListPlot[
{c[t, v, a]},
PlotStyle -> {Black, PointSize[0.025]}
],          (*close list plot*)
PlotRange -> {{0, 250}, {0, 125}},
ImageSize -> Full,
AspectRatio -> Automatic,
AxesOrigin -> {0, 0},
AxesLabel -> {"x(t)", "y(t)"}
],          (*close show*)
{{t, 0.00001, "Elapsed Time (seconds)"}, 0.00001, 10, Appearance -> "Labeled"},
{{v, 50, "Initial velocity (m/s)"}, 1, 50, Appearance -> "Labeled"},
{{a, 45, "Initial angle (degrees)"}, 1, 90, Appearance -> "Labeled"},
Delimiter, SaveDefinitions -> True
]          (*close manipulate*)


1) In the following code, I want to Animate just the Elapsed Time (t) variable. How do I write an Animate inside the Manipulate?

2) How do I have the graph not show until the Animation? I want the red line to advance along with the ball, not just have the ball follow the red line's already shown path. f[t_, v_, a_] :=v*Cos[a Degree]*t (the x value at time t) g[t_, v_, a_] :=v*Sin[a Degree]*t - (9.82*t^2)/2 (the y value at time t) c[t_, v_, a_] := {f[t, v, a],Max[g[t, v, a], 0]} (the x and y value at time t) xmax[v_, a_] := (v^2*Sin[2*a])/9.8 (x value when ball hits ground) ymax[v_, a_] := (v^2*(Sin^2)[a])/19.6 (maximum height) tmax[v_, a_] := (v*Sin[a Degree]/4.9) (time when ball hits ground)

    Manipulate[
Show[
ParametricPlot[
{f[t, v, a], Max[g[t, v, a], 0]}, {t, 0, 20},
PlotStyle -> {Thick, Red}
],          (*close parametric plot*)
ListPlot[
{c[t, v, a]},
PlotStyle -> {Black, PointSize[0.025]}
],          (*close list plot*)
PlotRange -> {{0, 250}, {0, 125}},
ImageSize -> Full,
AspectRatio -> Automatic,
AxesOrigin -> {0, 0},
AxesLabel -> {"x(t)", "y(t)"}
],          (*close show*)
{{t, 0.00001, "Elapsed Time (seconds)"}, 0.00001, 10, Appearance -> "Labeled"},
{{v, 50, "Initial velocity (m/s)"}, 1, 50, Appearance -> "Labeled"},
{{a, 45, "Initial angle (degrees)"}, 1, 90, Appearance -> "Labeled"},
Delimiter, SaveDefinitions -> True
]          (*close manipulate*)


1) In the following code, I want to Animate just the Elapsed Time (t) variable. How do I write an Animate inside the Manipulate?

2) How do I have the graph not show until the animation? I want the red line to advance along with the ball, not just have the ball follow the red line's already shown path.

f[t_, v_, a_] :=v*Cos[a Degree]*t        (*the x value at time t*)
g[t_, v_, a_] :=v*Sin[a Degree]*t - (9.82*t^2)/2 (*the y value at time t*)
c[t_, v_, a_] := {f[t, v, a],Max[g[t, v, a], 0]} (*the x and y value at time t*)
xmax[v_, a_] := (v^2*Sin[2*a])/9.8   (*x value when ball hits ground*)
ymax[v_, a_] := (v^2*(Sin^2)[a])/19.6   (*maximum height*)
tmax[v_, a_] := (v*Sin[a Degree]/4.9)  (*time when ball hits ground*)

Manipulate[
Show[
ParametricPlot[
{f[t, v, a], Max[g[t, v, a], 0]}, {t, 0, 20},
PlotStyle -> {Thick, Red}],          (*close parametric plot*)
ListPlot[
{c[t, v, a]},
PlotStyle -> {Black, PointSize[0.025]}
],          (*close list plot*)
PlotRange -> {{0, 250}, {0, 125}},
ImageSize -> Full,
AspectRatio -> Automatic,
AxesOrigin -> {0, 0},
AxesLabel -> {"x(t)", "y(t)"}
],          (*close show*)
{{t, 0.00001, "Elapsed Time (seconds)"}, 0.00001, 10, Appearance -> "Labeled"},
{{v, 50, "Initial velocity (m/s)"}, 1, 50, Appearance -> "Labeled"},
{{a, 45, "Initial angle (degrees)"}, 1, 90, Appearance -> "Labeled"},
Delimiter, SaveDefinitions -> True
]          (*close manipulate*)

1

# How do I animate just one variable out of three inside Manipulate/Not show line until Animate?

1) In the following code, I want to Animate just the Elapsed Time (t) variable. How do I write an Animate inside the Manipulate?

2) How do I have the graph not show until the Animation? I want the red line to advance along with the ball, not just have the ball follow the red line's already shown path. f[t_, v_, a_] :=v*Cos[a Degree]*t (the x value at time t) g[t_, v_, a_] :=v*Sin[a Degree]*t - (9.82*t^2)/2 (the y value at time t) c[t_, v_, a_] := {f[t, v, a],Max[g[t, v, a], 0]} (the x and y value at time t) xmax[v_, a_] := (v^2*Sin[2*a])/9.8 (x value when ball hits ground) ymax[v_, a_] := (v^2*(Sin^2)[a])/19.6 (maximum height) tmax[v_, a_] := (v*Sin[a Degree]/4.9) (time when ball hits ground)

    Manipulate[
Show[
ParametricPlot[
{f[t, v, a], Max[g[t, v, a], 0]}, {t, 0, 20},
PlotStyle -> {Thick, Red}
],          (*close parametric plot*)
ListPlot[
{c[t, v, a]},
PlotStyle -> {Black, PointSize[0.025]}
],          (*close list plot*)
PlotRange -> {{0, 250}, {0, 125}},
ImageSize -> Full,
AspectRatio -> Automatic,
AxesOrigin -> {0, 0},
AxesLabel -> {"x(t)", "y(t)"}
],          (*close show*)
{{t, 0.00001, "Elapsed Time (seconds)"}, 0.00001, 10, Appearance -> "Labeled"},
{{v, 50, "Initial velocity (m/s)"}, 1, 50, Appearance -> "Labeled"},
{{a, 45, "Initial angle (degrees)"}, 1, 90, Appearance -> "Labeled"},
Delimiter, SaveDefinitions -> True
]          (*close manipulate*)


Thank you for your assistance.