Shoot !

Shoot !

3 points

3 points NBA

Panier réussi !
     Bravo !!

Panier réussi !
     Bravo !!

    Raté !
Try Again !!

    Raté !
Try Again !!

Afficher la trajectoire du ballon du basketteur

p = 7.23 (slider from 0.75 to 10, step 0.01)
h = 2.75 (slider from 0 to 3.25, step 0.01)
v = 29.8 (slider from 0 to 50, step 0.1)
α = 0.8901179185171081 rad (slider from 0 to 80*°, step 0.0174532925199433)
f(x) = ((-4.9) * x^(2) / ((v / 3.6 * cos(α)))^(2)) + (tan(α) * x) + h
P: (p + 0.45, 0)
P_2: (x(P), 3.95)
a = Segment(P, P_2)
A = Intersect(f, a)
n: x = x(A) - 0.248
I = Intersect(f, n)
t_r: x(I) / ((v / 3.6 * cos(α)))
e = OrthogonalLine(A, a)
D = Point(e)
d = CurveCartesian(((v / 3.6 * cos(α)) * u), ((-4.9) * u^(2)) + ((v / 3.6 * sin(α)) * u) + h, u, 0, t_r)
i = Tangent(A, d)
C = Point(i)
β = Angle(C, A, D)
T(x) = t_r + (x(I) - x) / ((v / 3.6 * cos(β)))
f_1(x) = ((-4.9) * (T(x)^(2) - t_r^(2))) - ((v / 3.6 * sin(β)) * (T(x) - t_r)) + y(I)
K = Intersect(f_1, xAxis, 1)
t = 0 (slider from 0 to t_f, step 0.001)
t_A: x(A) / ((v / 3.6 * cos(α)))
x_B: ((v / 3.6 * cos(α)) * t)
z_B: ((-4.9) * t^(2)) + ((v / 3.6 * sin(α)) * t) + h
x_1: ((-tan(α)) - sqrt(tan(α)^(2) - ((4 * ((-4.9)) / ((v * cos(α) / 3.6))^(2)) * (h - 3.05)))) / ((2 * ((-4.9)) / ((v * cos(α) / 3.6))^(2)))
x_0: ((-tan(α)) - sqrt(tan(α)^(2) - ((4 * ((-4.9)) / ((v / 3.6 * cos(α)))^(2)) * h))) / ((2 * ((-4.9)) / ((v / 3.6 * cos(α)))^(2)))
B: (x_B, z_B)
t_0: x_0 / ((v / 3.6 * cos(α)))
t_1: x_1 / ((v / 3.6 * cos(α)))
P_1: (x(P), 3.05)
P_3: (x(P_1) - 0.9, 3.05)
b = Segment(P_3, P_1)
texte1: "Temps = " + t + " s"
texte2: "Détente = " + h + " m"
texte3: "Vitesse = " + v + " km/h"
texte4: "Angle = " + α + ""
P_4: (x(P_3) + 0.2, y(P_3) - 0.7)
P_5: (x(P_1) - 0.2, y(P_1) - 0.7)
poly1, p_3, p_4, p_5, p_1 = Polygon(P_3, P_4, P_5, P_1)
A1: x(A)
x_r: (((-(v / 3.6)) * cos(β)) * (t - t_r)) + x(I)
z_r: ((-4.9) * (t^(2) - t_r^(2))) - ((v / 3.6 * sin(β)) * (t - t_r)) + y(I)
B_r: (x_r, z_r)
k = 0 (slider from 0 to t_3, step 0.001)
x'_B: ((v / 3.6 * cos(α)) * k)
z'_B: ((-4.9) * k^(2)) + ((v / 3.6 * sin(α)) * k) + h
B': (x'_B, z'_B)
m = OrthogonalLine(P, xAxis)
G = Intersect(f, m)
c_1 = Circle(B_r, 0.248)
texte6: "Temps = " + k + " s"
H: (0, h)
H_1: ((v / ((3.6 * 5)) * cos(α)), h + (v / ((3.6 * 5)) * sin(α)))
u = Vector(H, H_1)
c_2 = Circle(B', 0.248)
d' = CurveCartesian(((v / 3.6 * cos(α)) * u), ((-4.9) * u^(2)) + ((v / 3.6 * sin(α)) * u) + h, u, 0, t_r)
t_F: t_r + (x(I) - x(K)) / ((v / 3.6 * cos(β)))
d_1 = CurveCartesian((((-(v / 3.6)) * cos(β)) * (u - t_r)) + x(I), ((-4.9) * (u^(2) - t_r^(2))) - ((v / 3.6 * sin(β)) * (u - t_r)) + y(I), u, t_r, t_F)
F = Intersect(f_1, l, (6.449276196277637, 0.2499999999981537))
t_f: t_r + (x(I) - x(F)) / ((v / 3.6 * cos(β)))
J = Intersect(f, g, 2)
t_3: x(J) / ((v / 3.6 * cos(α)))
c = Circle(B, 0.248)
texte8: "Position panier = " + p + " m"
E = (7.2, 0)
L = (7.680000000000001, 0)
M, N = Intersect(b, d_1)
O, Q = Intersect(b, d)
j = OrthogonalLine(P_3, b)
R = Intersect(j, d)
q = Function(((-0.18) * x^(2)) + (1.23 * x) + 2.75, 0, p)
texte14: "f(x)=" + (LaTeX[q]) + ""
o = false