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MathGroup Archive 2000

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Re: Parametric Solving Question From 14 Year Old

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23531] Re: Parametric Solving Question From 14 Year Old
  • From: Ronald Bruck <bruck at math.usc.edu>
  • Date: Tue, 16 May 2000 22:30:02 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In article <8fqr85$h40 at smc.vnet.net>, Alan <alana at mac.com> wrote:

: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.

[Because the email above was sent with some 8bit characters
 it is possible that the missing Degree mentioned below did not
 get transmitted. -- moderator]

Be careful, you may not get what you expect--Mathematica computes 
Cos[60] to be negative, because that's sixty RADIANS.  Use 1.0472 (60 
degrees in radians), or write it as 60 Degree (which will do the 
conversion).

To solve the second equation for t, do something like

x[t_] = 15 t Cos[60 Degree];
y[t_] = 15 t Sin[60 Degree] - 9.80665/2 t^2

(you can also refer to the 9.8066 as GravityAcceleration, if you load the
"Miscellaneous`StandardAtmosphere`" package).  Then

sol = Solve[y[t] == 0,t]

returns

{{t -> 0.}, {t -> 2.6493}}

The first solution is obvious, and the second is what you want.
To get the range, type

x[t]/.sol[[2]]

to get 19.8698.  (Not a very powerful projectile.)

But at age 14, instead of using Mathematica, you should be solving the 
quadratic equation by hand.  You're much better off reading an algebra 
book and playing with things by hand than using a CAS at this age.  

When I was your age, I was solving cubic equations, because I read 
"Algebra for the Practical Man", which showed how.  I didn't understand 
the REASON the solution worked, but understanding comes later.  Nor will 
I comment on how useful symbolic solutions to cubic equations are to the 
"Practical" man...

--Ron Bruck

-- 
Due to University fiscal constraints, .sigs may not be exceed one
line.


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