v_{0x} =

y_0  =

v_{0y} =

HOP

Wurfzeiten

Max/Auf

Einstellung

Geschwindigkeiten

P(x|y)

v_0 =

α =

α_b =

α =

g =

Schiefer Wurf - 1

Version Stand
14.03.2024
Andreas Jäger

Stand

v_x(x)

v_y(x)

v_0(x)

Soll

g: 10
v0y: 20
v0x: 10
y0: 10
vyMax: v0y - ((v0x * v0y) - (v0x * sqrt(v0y^(2) + ((2 * g) * y0)))) / v0x
PN1: (0, 0)
PN2: PN1
Py0: (0, y0)
Pxy: (v0x, v0y + y0)
f(x) = y0 + (v0y / v0x * x) - (g / ((2 * v0x^(2))) * x^(2))
x1: ((v0x * v0y) + (v0x * sqrt(v0y^(2) + ((2 * g) * y0)))) / g
f0(x) = If[0 ≤ x ≤ x1, f(x)]
u = Vector(Py0, Pxy)
Eingabefeld1 = Textfield(v0x)
Eingabefeld2 = Textfield(y0)
Eingabefeld3 = Textfield(v0y)
P1: (x1, 0)
xMax: ((v0x * v0y)) / g
tMax: v0y / g
t1: (v0y + sqrt(v0y^(2) + ((2 * g) * y0))) / g
gl1 = If(text ≟ "HOP", text = "Rand")
gl2 = If(text ≟ "HOP", text = "Rand")
gl3 = If(text ≟ "HOP", text = "Rand")
gl4 = If(text ≟ "HOP", text = "Rand")
b1: false
nX = 1
bX = true
n = 6 (slider from 2 to 10, step 1)
dt: t1 / (n - 1)
l1 = Sequence(((t * v0x), (-(((g * t^(2))) / 2)) + (t * v0y) + y0), t, 0, t1, dt)
bt: false
Pmax: (Max[0, xMax], If[xMax ≤ 0, y0, f(xMax)])
Text4: "n = " + n + ""
v00 = 22.360679774997898 (slider from 0 to 40, step 0.01)
bv: false
vx(x) = If[0 ≤ x ≤ x1, v0x]
vy(x) = If[0 ≤ x ≤ x1, v0y - (g * x / v0x)]
vv(x) = sqrt((vx(x))^(2) + (vy(x))^(2))
Text6: "\text{\underline{Geschwindi}}\text{g}\text{\underline{keiten:}}\cr
v_{0x}=" + (LaTeX[v0x]) + "\ {m\over s}\cr
v_{0y}=" + (LaTeX[v0y]) + "\ {m\over s}\cr
v_{0}\ =" + (LaTeX[sqrt(v0x^(2) + v0y^(2))]) + "\ {m\over s}"
Text5: "\text{\underline{Zeiten}}\cr
Δt =  " + (LaTeX[dt]) + " \ s\cr
t_{Max}=" + (LaTeX[tMax]) + "\ s\cr
t_{Auf}=" + (LaTeX[t1]) + "\ s"
xx = 0 (slider from 0 to 100, step 0.01)
XX: (xx, 0)
XY: xx
yy: f(xx)
vY = Vector((xx, yy), (xx, yy + v0y - (g * xx / v0x)))
vX = Vector((xx, yy), (xx + v0x, yy))
vV = Vector((xx, yy), (xx + v0x, yy + v0y - (g * xx / v0x)))
YY: (xx, yy)
bP = false
Eingabefeld4 = Textfield(v00)
alpha = 1.1071487177940904 (slider from -1.57 to 1.57, step 0.01)
Eingabefeld5 = Textfield(alpha)
alphab = 1.1071487177940904 (slider from -1.55 to 1.55, step 0.01)
Eingabefeld6 = Textfield(alphab)
alphaE = 45 (slider from -45 to 45, step 0.01)
Eingabefeld7 = Textfield(alphaE)
Eingabefeld8 = Textfield(g)
a = false
Text7: "\text{\underline{Werte am Punkt P}\cr
x_P = " + (LaTeX[xx]) + "\ m\cr
y_P\ =\ " + (LaTeX[yy]) + "\ m\cr
\alpha\ \ =\ " + (LaTeX[(360 / ((2 * pi)) * atan((v0y - (g * xx / v0x)) / v0x))]) + "\degree\cr
v_x =  " + (LaTeX[v0x]) + "\ {m\over s}\cr
v_y =  " + (LaTeX[v0y - (g * xx / v0x)]) + "  \ {m\over s}\cr
|v| =  " + (LaTeX[sqrt(v0x^(2) + (v0y - (g * xx / v0x))^(2))]) + "\ {m\over s}\cr"
Text1: "\text{\underline{Höchster Punkt:}\cr
x_{max}\ =\ " + (LaTeX[Max[0, xMax]]) + "\ m\cr
y_{max}\ = " + (LaTeX[If[xMax ≥ 0, f(xMax), y0]]) + "\ m\cr
t_{max}\ =\ " + (LaTeX[Max[0, tMax]]) + "\ s\cr
\ \cr
\underline{\text{Auf}}{\text{p}}\underline{\text{rallort}}\cr 
x_{Auf} = " + (LaTeX[x1]) + "\ m\cr
y_{Auf} = 0\cr
t_{Auf} = " + (LaTeX[t1]) + "\ s"