v_0

v_0\cdot\cos\alpha

v_0\cdot\sin\alpha

x=t\cdot v_0\cdot\cos\alpha

\overline{y}=t\cdot v_0\cdot \sin\alpha

\frac{1}{2}\!\cdot\! g\!\cdot\! t^2

y=t\!\cdot\! v_0\!\cdot\! \sin\alpha-\frac{1}{2}\!\cdot\! g\!\cdot\! t^2

x

y

\textrm{\textbf{Vrh šikmý vzhůru}}\
\vspace{0.8cm}
\textrm{Pokud zanedbáme odpor vzduchu (ve vakuu), je trajektorií hmotného bodu \textbf{parabola}.}

\textrm{Souřadnice }[\,x,y\,]\textrm{ jejího bodu jsou popsány rovnicemi:}\
x=t\cdot v_0\cdot \cos\alpha\
y=t\cdot v_0\cdot \sin\alpha-\frac{1}{2}\!\cdot\! g\!\cdot\! t^2

t=\frac{x}{v_0\cdot\cos\alpha}\
\vspace{1cm}
y=x\cdot \textrm{tg\,}\alpha-\frac{g}{2\cdot v_0^2\cdot\cos^2\alpha}\cdot x^2\dots\textrm{rovnice paraboly}

\textrm{Polohu vrcholu najdeme, položíme-li  }y'=0:\
\vspace{0.8cm}
y'=\textrm{tg\,}\alpha-\frac{g}{v_0^2\cdot\cos^2\alpha}\cdot x=0\
\vspace{1.5cm}
x=\frac{v_0^2\cdot\sin\alpha\cdot\cos\alpha}{g}=\frac{v_0^2\cdot\sin2\alpha}{2g}

\textrm{Odtud vidíme, že maximální délku vrhu získáme pro } \sin2\alpha\!=\!1,\
\textrm{což nastane, je-li úhel }\alpha\!=\!45°

\textrm{Těleso dosáhne vrcholu v čase:}\
\vspace{0.8cm}
t=\frac{v_0\cdot\sin\alpha}{g}

X_1 = Point(xAxis)
X_2 = Point(xAxis)
Y_2 = Point(yAxis)
Y_1 = Point(yAxis)
u = Vector(X_1, X_2)
v = Vector(Y_1, Y_2)
c: y = x - (2 / 5 * x^(2))
a = Segment(X_1, X_2)
b = Segment(Y_1, Y_2)
O, O' = Intersect(c, a)
d = Segment(O, O')
P_1 = Point(d)
e = OrthogonalLine(P_1, d)
P_2 = Intersect(c, e)
množina1 = Locus(P_2, P_1)
O'' = Rotate(O', 45°, O)
f = Segment(O, O'')
O''' = Point(f)
w = Vector(O, O''')
g = OrthogonalLine(O''', u)
h = OrthogonalLine(O''', v)
O_2 = Intersect(h, b)
O_1 = Intersect(a, g)
i = Vector(O, O_2)
j = Vector(O, O_1)
k = Segment(O_2, O''')
l = Segment(O''', O_1)
m = Segment(X_1, O)
n = Segment(O, Y_1)
α = Angle(a, f)
S = Point(množina1)
p = OrthogonalLine(S, a)
q = OrthogonalLine(S, b)
B = Intersect(f, p)
r = OrthogonalLine(B, b)
S_2 = Point(a)
s = OrthogonalLine(S_2, a)
S_2' = Intersect(r, s)
S_1 = Point(b)
t = OrthogonalLine(S_1, b)
S_1' = Intersect(t, p)
S_3 = Point(a)
a_1 = OrthogonalLine(S_3, a)
S_3' = Intersect(q, a_1)
S_3'' = Intersect(r, a_1)
u_1 = Vector(S_1, S_1')
v_1 = Vector(S_1', S_1)
S' = Intersect(a, p)
S''' = Intersect(r, b)
S'' = Intersect(q, b)
b_1 = Segment(S, S')
c_1 = Segment(S'', S)
S_1'' = Point(p)
d_1 = Segment(S', S_1'')
S_2'' = Point(r)
e_1 = Segment(S_2'', S''')
w_1 = Vector(S_2, S_2')
f_1 = Vector(S_2', S_2)
g_1 = Segment(S''', B)
h_1 = Segment(B, S)
S_4 = Point(q)
i_1 = OrthogonalLine(S_4, q)
S_4' = Intersect(r, i_1)
j_1 = Segment(B, S_4')
k_1 = Segment(S, S_4)
l_1 = Vector(S_3, S_3')
m_1 = Vector(S_3', S_3)
n_1 = Vector(S_3', S_3'')
p_1 = Vector(S_3'', S_3')
q_1 = Vector(O_2, Y_2)
r_1 = Vector(O_1, X_2)
Z_1: (-4, 5)
s_1 = Line(Z_1, q_1)
Z_2: (-0.5, 4.4)
t_1 = Line(Z_2, q_1)