nomor 9 dan nomor 10 dong tolonf

[tex]\displaystyle 9\\\theta=45^\circ\\h=30\,\text{m}\\v=20\,\text{m/s}\\g=10\,\text{m/s}^2\\\\x=?\\\\v_{y-\text{max}}^2=v_{0y}^2-2gh_{\text{max}}\\0^2=(20\sin45^\circ)^2-2(10)h_{\text{max}}\\20h_{\text{max}}=200\\h_{\text{max}}=10\,\text{m}\\\\v_{y-\text{max}}=v_{0y}-gt_{\text{max}}\\0=20\sin45^\circ-10t_{\text{max}}\\10t_{\text{max}}=10\sqrt2\\t_{\text{max}}=\sqrt2\,\text{s}\\\\s_x=v_x\cdot t_{\text{max}}\\s_x=20\cos45^\circ\cdot\sqrt2\\s_x=20\,\text{m}[/tex]

[tex]\displaystyle v_{y-\text{min}}^2=v_{y-\text{max}}^2+2gh'\\v_{y-\text{min}}^2=0^2+2(10)(30+10)\\v_{y-\text{min}}^2=800\\v_{y-\text{min}}=20\sqrt2\,\text{m/s}\\\\v_{y-\text{min}}=v_{y-\text{max}}+gt\\20\sqrt2=0+10t\\2\sqrt2\,\text{s}=t\\\\s_x'=v_x\cdot t\\s_x'=20\cos45^\circ\cdot10\sqrt2\\s_x'=10\sqrt2\cdot2\sqrt2\\s_x'=40\,\text{m}\\\\x=s_x+s_x'\\x=20+40\\\boxed{\boxed{x=60\,\text{m}}}[/tex]


[tex]\displaystyle 10\\v_{0y}=5\,\text{m/s}\\v_x=100\,\text{m/s}\\h=100\,\text{m}\\\\x=?\\\\v_{y-\text{max}}^2=v_{0y}^2-2gh_{\text{max}}\\0^2=5^2-2(10)h_{\text{max}}\\20h_{\text{max}}=25\\h_{\text{max}}=1,25\,\text{m}\\\\v_{y-\text{max}}=v_{0y}-gt\\0=5-10t\\10t=5\\t=0,5\,\text{s}\\\\s_x=v_xt\\s_x=100\cdot0,5\\s_x=50\,\text{m}[/tex]

[tex]\displaystyle v_{y-\text{min}}^2=v_{y-\text{max}}^2+2gh'\\v_{y-\text{min}}^2=0^2+2(10)(100+1,25)\\v_{y-\text{min}}^2=2025\\v_{y-\text{min}}=45\,\text{m/s}\\\\v_{y-\text{min}}=v_{y-\text{max}}+gt'\\45=0+10t'\\4,5\,\text{s}=t'\\\\s_x'=v_x\cdot t'\\s_x'=100\cdot4,5\\s_x'=450\,\text{m}\\\\x=s_x+s_x'\\x=50+450\\\boxed{\boxed{x=500\,\text{m}}}[/tex]

9][ GP
V₀ = 20 m/s
α = 45°
g = 10 m/s²
Y₀ = 30 m
Y = 0 → X = __?

gerak arah vertikal
Y = Y₀ + V₀ sin α t - ½ g t²
0 = 30 + 20 • sin 45° • t - ½ • 10 • t²
0 = 30 + 20 • ½√2 • t - 5 t²
0 = 30 + 10√2 t - 5 t²
5 t² - 10√2 t - 30 = 0
t² - 2√2 t - 6 = 0
t₁₂ = [2√2 ± √((-2√2)² - 4•1•(-6))] / 2
t₁₂ = [2√2 ± √(8 + 24)] / 2
t₁₂ = [2√2 ± 4√2] / 2
t = -√2 [TM] atau t = 3√2 s

gerak arah horizontal
X = V₀ cos α t
X = 20 • cos 45° • 3√2
X = 20 • ½√2 • 3√2
X = 60 m ← jwb


10][
Vy = 5 m/s
Vx = 100 m/s
g = 10 m/s²
Y₀ = 100 m
Y = 0 → X = __?

gerak arah vertikal
Y = Y₀ + Vy t - ½ g t²
0 = 100 + 5 • t - ½ • 10 • t²
0 = 100 + 5 t - 5 t²
5 t² - 5 t - 100 = 0
t² - t - 20 = 0
(t + 4) (t - 5) = 0
t = - 4 [TM] atau t = 5 s

gerak arah horizontal
X = Vx t
X = 100 • 5
X = 500 m ← jwb