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