Re: Parametric Solving Question From 14 Year Old
- To: mathgroup at smc.vnet.net
- Subject: [mg23534] Re: [mg23507] Parametric Solving Question From 14 Year Old
- From: BobHanlon at aol.com
- Date: Tue, 16 May 2000 22:30:05 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 5/16/2000 3:06:22 AM, alana at mac.com writes:
> I am 14 and am wondering how to solve parametric equations directly
>without graphing in Mathematica? I am figuring out when a projectile in
>motion hits the ground only due to the even force of gravity acting upon
>it. The parametric equation is:
>
>x(t)=15*t*Cos[60]
>y(t)=15*t*Sin[60]-9.80665/2*t^2
>
>I want to find the value x(t) and t when y(t)=0.
>
x[t_] := Evaluate[15*t*Cos[60 Degree]];
y[t_] := Evaluate[15*t*Sin[60 Degree] - 9.80665/2*t^2];
Note that arguments to trig functions must be given in radians. Angles given
in degrees need to be multiplied by Degree to convert the argument to radians.
tmax = Max[t /. Solve[y[t] == 0, t]]
2.6493
xmax = x[tmax]
19.8698
Plot[{x[t], y[t]}, {t, 0, tmax},
PlotStyle -> {RGBColor[0, 0, 1], RGBColor[1, 0, 0]}, PlotRange -> All,
AxesLabel -> {"t", {StyleForm["x[t]", FontColor -> RGBColor[0, 0, 1]],
StyleForm["y[t]", FontColor -> RGBColor[1, 0, 0]]}}];
y[t /. Solve[x == x[t], t]]
{Sqrt[3]*x - 0.0871702*x^2}
Plot[%, {x, 0, xmax}, PlotStyle -> RGBColor[1, 0, 0],
AxesLabel -> {"x", StyleForm["y[x]", FontColor -> RGBColor[1, 0, 0]]}];
Bob
BobHanlon at aol.com