Golf
Author: Daniel Mentrard
Date: Janvier 2008

Adjust shooting parameters (initial speed, angle, etc. ..)

v_0

Not bad at all

Start

New

t = 11 (slider from 0 to 11, step 0.001)
α = 1.0122909661567112 rad (slider from 0 to 1.5707963267948966, step 0.017453292519943295)
v_0 = 37.3 (slider from 10 to 100, step 0.1)
g = 9.809999999999999 (slider from 1 to 20, step 0.01)
x_M: v_0^(2) * sin(2 * α) / g
A = Intersect(xAxis, yAxis)
c = Circle(A, 1)
B = Intersect(c, xAxis, 2)
C = Rotate(B, α, A)
a = Segment(A, C)
d = Circle(C, 0.2)
b = OrthogonalLine(C, a)
D, E = Intersect(d, b)
e = Circle(A, 0.3)
F = Intersect(e, xAxis, 1)
G, H = Intersect(e, xAxis)
g_3 = Circle(A, 0.2)
h = Line(E, a)
I = Intersect(g_3, h, 1)
i = Segment(E, I)
j = Segment(E, C)
k = Line(D, h)
J = Intersect(g_3, k, 1)
l = Segment(D, J)
K = Intersect(l, xAxis)
M = Point(xAxis)
N = (-60, -30)
O = (100, -30)
P = Point(xAxis)
Q = (99.61948548898192, 38.554047870219435)
R = (-60.004681359060946, 38.554047870219435)
s: y = x * tan(α) - 0.5 * g / (v_0^(2) * cos(α)^(2)) * x^(2)
W, Z = Intersect(s, xAxis)
Distance = Segment(W, Z)
h_1: v_0^(2) * sin(α)^(2) / (2 * g)
b_1 = LineBisector(W, Z)
x_1: v_0 * cos(α) * t
y_1: v_0 * sin(α) * t - 0.5 * g * t^(2)
X_0: (If[x_1 ≤ Distance, x_1, Distance], If[x_1 ≤ Distance, y_1, 0])
t_1 = OrthogonalLine(X_0, Distance)
C_1 = Intersect(Distance, t_1)
g_1 = Segment(X_0, C_1)
t_m: 2 * v_0 * sin(α) / g
T2: "t_m= { " + t_m + " }"
U_1: v_0^(2) / (2 * g)
H_2: (0, U_1)
u = If(α < 90, 0, H_2)
H_M = If(α ≟ 90°, H_2)
j_1 = Segment(H_M, A)
T4: "Longueur=" + x_M + "m"
T6: "H_M=" + h_1
v_1 = Vector(W, W + (v_0 / 4 * cos(α), v_0 / 4 * sin(α)))
f(x) = x * tan(α) - 0.5 * g / (v_0^(2) * cos(α)^(2)) * x^(2)
m = Tangent(X_0, f)
p = Circle(X_0, v_0 / 4)
L, S = Intersect(p, m)
v = Vector(X_0, S)
f1 = Function(f, 0, Distance)
T5: "v_0 = " + v_0 + " m/s"
T7: "α = " + α
T8: "g = " + g + " N/kg"
H1 = Point(xAxis)
I1 = Point(xAxis)
J1 = Point(xAxis)
K1 = (320.73684084230683, -84.16494562455907)
L1 = (-147.76636642530644, -79.27687042834802)
poly5, i1, j1, k1, l1 = Polygon(I1, J1, K1, L1)
T: (random() * 100 + 80, 0)
C1: (x(X_0), y(T))
U = Point(xAxis)
β = Angle(U, W, W + (v_0 / 4 * cos(α), v_0 / 4 * sin(α)))