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RE: Parametric Solving Question From 14 Year Old
*To*: mathgroup at smc.vnet.net
*Subject*: [mg23528] RE: [mg23507] Parametric Solving Question From 14 Year Old
*From*: "David Park" <djmp at earthlink.net>
*Date*: Tue, 16 May 2000 22:29:59 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
> From: Alan [mailto:alana at mac.com]
To: mathgroup at smc.vnet.net
> Hello!
> 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.
>
> Thank you,
> Alan
>
Alan,
First you have to define x and y as functions in the Mathematica language. I
have changed the parameters in your parametric equations, so you can try it
out youself with your actual values.
x[t_] := 20 t Cos[30Degree];
y[t_] := 20 t Sin[30 Degree] - 9.80665/2 t^2
Then you can use Solve to solve your equations. If all you wish to know is
when the projectile will hit the ground, you don't even need the x function.
tsols = Solve[y[t] == 0]
{{t -> 0.}, {t -> 2.03943}}
You obtain two solutions because it is a quadratic equation. The second
solution is the one you want. The first solution corresponds to the fact
that the projectile was at ground level when it was launched. If you wish to
also know where the projectile hit the ground, you can substitute the second
solution into the x function.
x[t] /. tsols[[2]]
35.324
If you are new to Mathematica, be sure to read Section 1.7.1 Defining
Functions, Section 1.5.7 Solving Equations and Section 1.4.2 Values for
Symbols in the Mathematica Book.
Gee, I wish I had Mathematica when I was 14 years old!
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
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