Trajectoires

Enveloppe

Mo

vo = 10 (slider from 0 to 100, step 5)
h: vo^(2) / 20
ze = Function(h - x^(2) / 4 / h, 0, 2 * h)
α = 1.46 rad (slider from 0 to 1.57, step 0.02)
a: -1 / (4 * h) * (1 + tan(α)^(2))
b: tan(α)
z = Function(a * x^(2) + b * x, 0, (-b) / a)
S: ((-b) / (2 * a), z((-b) / (2 * a)))
A = Point(z)
B = Point(z)
Mo = (10, 0)
xo: x(Mo)
zo: y(Mo)
Δ: xo^(2) - 4 * xo^(2) / 4 / h * (zo + xo^(2) / 4 / h)
A1: (xo + sqrt(Δ)) / (2 * xo^(2) / 4 / h)
z1(x) = (-1) / 4 / h * (1 + A1^(2)) * x^(2) + A1 * x
A2: (xo - sqrt(Δ)) / (2 * xo^(2) / 4 / h)
z2(x) = (-1) / 4 / h * (1 + A2^(2)) * x^(2) + A2 * x
za1 = If(z1(x) ≥ 0, z1)
za2 = If(z2(x) ≥ 0, z2)
c = true
d = true
e = true