Lösung anzeigen

A = Intersect(xAxis, yAxis)
A1 = (0.07354166666666705, -0.06381944444444419)
A2 = (0.13500000000000037, -0.13361111111111085)
A3 = (0.22666666666666704, -0.20444444444444418)
A5 = (0.5266666666666671, -0.37111111111111084)
A6 = (0.7100000000000004, -0.4919444444444442)
A7 = (0.955, -0.6222222222222222)
A8 = (1.2572222222222222, -0.7333333333333333)
A9 = (1.5194444444444444, -0.8266666666666667)
A10 = (1.7725000000000004, -0.9086111111111108)
B = (2, -1)
g = 9.81
v0 = 0
g1: g * (y(A1) - y(A)) / Distance[A1, A]
g2: g * (y(A2) - y(A1)) / Distance[A2, A1]
g3: g * (y(A3) - y(A2)) / Distance[A3, A2]
A4 = (0.364166666666667, -0.28361111111111087)
g4: g * (y(A4) - y(A3)) / Distance[A4, A3]
g5: g * (y(A5) - y(A4)) / Distance[A5, A4]
g6: g * (y(A6) - y(A5)) / Distance[A6, A5]
g7: g * (y(A7) - y(A6)) / Distance[A7, A6]
g8: g * (y(A8) - y(A7)) / Distance[A8, A7]
g9: g * (y(A9) - y(A8)) / Distance[A9, A8]
g10: g * (y(A10) - y(A9)) / Distance[A10, A9]
g11: g * (y(B) - y(A10)) / Distance[B, A10]
v1: sqrt(-2.0 * g * y(A1))
v2: sqrt(-2.0 * g * y(A2))
v3: sqrt(-2.0 * g * y(A3))
v4: sqrt(-2.0 * g * y(A4))
v5: sqrt(-2.0 * g * y(A5))
v6: sqrt(-2.0 * g * y(A6))
v7: sqrt(-2.0 * g * y(A7))
v8: sqrt(-2.0 * g * y(A8))
v9: sqrt(-2.0 * g * y(A9))
v10: sqrt(-2.0 * g * y(A10))
t2 = If(g2 ≟ 0.0, Distance[A1, A2] / v1, v1 / g2 - abs(g2) / g2 * sqrt((v1 / g2)^(2.0) - 2.0 * Distance[A2, A1] / g2))
t1: v0 / g1 - abs(g1) / g1 * sqrt((v0 / g1)^(2.0) - 2.0 * Distance[A1, A] / g1)
t3 = If(g3 ≟ 0.0, Distance[A2, A3] / v2, v2 / g3 - abs(g3) / g3 * sqrt((v2 / g3)^(2.0) - 2.0 * Distance[A3, A2] / g3))
t4 = If(g4 ≟ 0.0, Distance[A3, A4] / v3, v3 / g4 - abs(g4) / g4 * sqrt((v3 / g4)^(2.0) - 2.0 * Distance[A4, A3] / g4))
t5 = If(g5 ≟ 0.0, Distance[A4, A5] / v4, v4 / g5 - abs(g5) / g5 * sqrt((v4 / g5)^(2.0) - 2.0 * Distance[A5, A4] / g5))
t6 = If(g6 ≟ 0.0, Distance[A5, A6] / v5, v5 / g6 - abs(g6) / g6 * sqrt((v5 / g6)^(2.0) - 2.0 * Distance[A6, A5] / g6))
t7 = If(g7 ≟ 0.0, Distance[A6, A7] / v6, v6 / g7 - abs(g7) / g7 * sqrt((v6 / g7)^(2.0) - 2.0 * Distance[A7, A6] / g7))
t8 = If(g8 ≟ 0.0, Distance[A7, A8] / v7, v7 / g8 - abs(g8) / g8 * sqrt((v7 / g8)^(2.0) - 2.0 * Distance[A8, A7] / g8))
t9 = If(g9 ≟ 0.0, Distance[A8, A9] / v8, v8 / g9 - abs(g9) / g9 * sqrt((v8 / g9)^(2.0) - 2.0 * Distance[A9, A8] / g9))
t10 = If(g10 ≟ 0.0, Distance[A9, A10] / v9, v9 / g10 - abs(g10) / g10 * sqrt((v9 / g10)^(2.0) - 2.0 * Distance[A10, A9] / g10))
t11 = If(g11 ≟ 0.0, Distance[A10, B] / v10, v10 / g11 - abs(g11) / g11 * sqrt((v10 / g11)^(2.0) - 2.0 * Distance[B, A10] / g11))
tsumme: t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 + t11
a = Line(A, B)
gg(x) = acos(1.0 - x) - sqrt(x * (2.0 - x))
i(x) = 2.0 * 3.141592653589793 - gg(x)
l(x) = -(x) * x(B) / y(B)
C = Intersect(i, l, (1.9334883051396201, 3.866976610278231))
D = Intersect(gg, l, (1.9975950495578911, 3.002913559264668))
Stauch: x(B) / y(D)
Stauch2: x(B) / y(C)
b = CurveCartesian(Stauch * (t - sin(t)), Stauch * (cos(t) - 1.0), t, 0.0, 6.283185307179586)
c = CurveCartesian(Stauch2 * (t - sin(t)), Stauch2 * (cos(t) - 1.0), t, 0.0, 6.283185307179586)
Text1: "Benötigte Zeit =" + tsumme
d = false