Hello,
I tried solving both equations separately, but I face an error everytime saying that the limiting value is not a machine sized number and a certain replacement rule is invalid. I cannot quite figure it where that error exists.
I used the below mentioned Projectile equations as suggested for the Trebuchet, but, cannot get the projectile to leave the Trebuchet.
Manipulate[
ParametricPlot[{{V Cos[\[Theta]] t,
V Sin[\[Theta]] t -
9.8 t^2/2}, {V vt Cos[\[Theta]]/9.8 (1 - Exp[-9.8 t/vt]),
vt/9.8 (V Sin[\[Theta]] + vt) (1 - Exp[-9.8 t/vt]) - vt t}}, {t,
0, tf}, PlotStyle -> {{Thick, Blue}, {Thick, Red}},
AxesOrigin -> {0, 0}, AxesLabel -> {x, z},
PlotRange -> {{0, 400}, {0, 300}}, ImageSize -> 500,
Epilog -> {Green, PointSize[.02],
Point[{{V Cos[\[Theta]] tf,
V Sin[\[Theta]] tf -
9.8 tf^2/2}, {V vt Cos[\[Theta]]/9.8 (1 - Exp[-9.8 tf/vt]),
vt/9.8 (V Sin[\[Theta]] + vt) (1 - Exp[-9.8 tf/vt]) -
vt tf}}]}], {{V, 48.8, "initial velocity"}, 1, 100,
Appearance -> "Labeled"}, {{\[Theta], 1.09, "angle"}, .1, \[Pi]/2,
Appearance -> "Labeled"}, {{vt, 100, "terminal velocity"}, .01, 300,
Appearance -> "Labeled"}, {{tf, 8.75, "time"}, .1, 17,
Appearance -> "Labeled"}]
How do I separately solve for the Trebuchet and the Projectile, so that I can get an animation where the projectile actually leaves the trebuchet?
Thanks.