Mathematica Tool 2

This Mathematica notebook is designed to be used with Activity 4 in Section 3.3

Needs["VectorFieldPlots`"]

Enter th value of g in feet per second per second

g=32.17;

Here is the slope field for this differential equation.

Slopefield=VectorFieldPlot[#/Norm[#]&[{1,g t}],{t,0,5},{v,0,200},Axes->True,ColorFunction->Hue,AspectRatio-> 1]

Part (b). Enter your formula for a solution to s(t) to the initial value problem in (b).

(Subscript[s, b])[t_]:=((g (t^2))/2)

Plot the graph on the slope field.

Plot1=Plot[(Subscript[s, b])[t],{t,0,5},PlotStyle->{Blue,Thickness[0.01]},PlotRange->{{0,5},{0,200}}];
Show[Slopefield,Plot1]

Part (c). Enter your formula for a solution to s(t) to the initial value problem in (c) and plot the graph  of both solutions on the slope field.

(Subscript[s, c])[t_]:=((g (t^2))/2)+10
Plot2=Plot[(Subscript[s, c])[t],{t,0,5},PlotStyle->{Green,Thickness[0.01]},PlotRange->{{0,5},{0,200}}];
Show[Slopefield,Plot1,Plot2]