       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
>y(t)=15*t*Sin-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*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

```

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