Zadania 39-48 Zróbcie tyle ile umiecie proszę

[latex]ZAD.39[/latex] [latex] left { {{ V_1=Vm-V_w= frac{8m}{2s}=4 frac{m}{s} } atop {V_2=Vm+V_w= frac{16m}{2s}=8 frac{m}{s}}} ight. [/latex] [latex] left { {{ Vm-V_w= 4 frac{m}{s} } atop {Vm+V_w= 8 frac{m}{s}}} ight. [/latex] [latex]left { {{ Vm=V_w+ 4 frac{m}{s} } atop {V_w+ 4 frac{m}{s}+V_w= 8 frac{m}{s}}} ight.[/latex] [latex]left { {{ Vm=V_w+ 4 frac{m}{s} } atop {2V_w = 4 frac{m}{s}}} ight.[/latex] [latex]left { {{ Vm=V_w+ 4 frac{m}{s} } atop {V_w = 2 frac{m}{s}}} ight.[/latex] [latex]Predkosc wody V_w=2frac{m}{s};predkosc motorowki V_1=4frac{m}{s} i V_2=8frac{m}{s}[/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.40[/latex]  [latex]Z prawa Pitagorasa V_w^2=V_1^2+V_2^2[/latex] [latex]V_2= sqrt{V_w^2-V_1^2}= sqrt{ (5frac{m}{s})^2 -(4 frac{m}{s})^2}=3 frac{m}{s}[/latex]    -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.41.Dane:[/latex] [latex]s_1=120m[/latex] [latex]s_2=230m[/latex] [latex]t=10s[/latex] [latex]V_2=36 frac{km}{h}=10 frac{m}{s} [/latex] [latex]V_1=V_w-V_2= frac{s_1+s_2}{t} -V_2= frac{120m+230m}{10s} -10 frac{m}{s}=25 frac{m}{s} [/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.42.Dane:[/latex] [latex]V_1=25 frac{m}{s} [/latex] [latex]V_2=20frac{m}{s} [/latex] [latex]s=0,5km=500m[/latex] [latex]t= frac{s}{V_w} = frac{s}{V_1-V_2}= frac{500m}{25 frac{m}{s} -20frac{m}{s} }=100s[/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.43.Dane:[/latex] [latex]s_1=260m[/latex] [latex]s_2=180m[/latex] [latex]t=8,3s[/latex] [latex]V_1=30 frac{m}{s} [/latex] [latex]V_2=V_w-V_1= frac{s_1+s_2}{t}-V_1= frac{260m+180m}{8,3s} -30 frac{m}{s}= 23,012 frac{m}{s} [/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.44.Dane:[/latex] [latex]d=12m[/latex] [latex]V_{rz}=2frac{m}{s} [/latex] [latex]t_{AB}=25s[/latex] [latex]b) [/latex] [latex]sin alpha = frac{V_{rz}}{V_k}= frac{1}{2} [/latex] [latex] alpha =30^o[/latex] [latex]c)[/latex] [latex]V_k=2*V_w=2*2 frac{m}{s}=4 frac{m}{s} [/latex] [latex]d)[/latex] [latex]t_1= frac{d}{V_k}= frac{12m}{4 frac{m}{s} } =3s[/latex] [latex]e)[/latex] [latex]s_{wianek}= V_{rz}*t_1=2 frac{m}{s} *3s=6m[/latex] [latex]f)[/latex] [latex]S_{AB}=(V{rz}+V_k)*t_{AB}=(2 frac{m}{s} +4frac{m}{s} )*25s=150m[/latex] [latex]g)[/latex] [latex]t_{BA}= frac{S_{AB}}{Vk-V{rz}}= frac{150m}{4frac{m}{s} -2frac{m}{s} }=75s[/latex] [latex]h)[/latex] [latex]t_{AB}=25s[/latex] [latex]S_{BA}=S_{AB}=150m[/latex] [latex]V_{sr}= frac{S_c}{t_c}= frac{S_{AB}+S_{BA}}{t_{AB}+t_B+t_{BA}}= frac{150m+150m}{25s+2,5*60s+75s}=1,2 frac{m}{s} [/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.45.Dane:[/latex] [latex]V_1=3 frac{m}{s} [/latex] [latex]V_2=5frac{m}{s} [/latex] [latex]t_1=10min=600s[/latex] [latex]t_2=30min=1800s[/latex] [latex]1.1[/latex] [latex]Sc=V_2*t_1+(V_2-V_1)*t_2=5 frac{m}{s}*600s + (5frac{m}{s} -3frac{m}{s})*1800s=6 600m[/latex] [latex]1.2[/latex] [latex] left { {{ Vm-V_w= 3 frac{m}{s} } atop {Vm+V_w=5 frac{m}{s}}} ight. [/latex] [latex]left { {{ Vm=V_w+ 3 frac{m}{s} } atop {V_w+ 3 frac{m}{s}+V_w= 5 frac{m}{s}}} ight.[/latex] [latex]left { {{ Vm=V_w+ 3 frac{m}{s} } atop {2V_w = 2 frac{m}{s}}} ight.[/latex] [latex]left { {{ Vm=V_w+ 3 frac{m}{s} } atop {V_w = 1 frac{m}{s}}} ight.[/latex] [latex]left { {{ Vm=1frac{m}{s}+ 3 frac{m}{s} } atop {V_w = 1 frac{m}{s}}} ight.[/latex] [latex]left { {{ Vm=4 frac{m}{s} } atop {V_w = 1 frac{m}{s}}} ight.[/latex] [latex]1.4[/latex] [latex]t_1= frac{ frac{S}{2} + frac{S}{2}}{V_m}= frac{S}{V_m} [/latex] [latex]t_2=t_{21}+t_{22}= frac{ frac{S}{2}}{Vm+V{rz}}+ frac{ frac{S}{2}}{Vm-V_{rz}}=[/latex] [latex]=frac{ frac{S}{2}*(Vm-V_{rz})}{(Vm+V{rz})*(Vm-V_{rz})}+ frac{ frac{S}{2}*(Vm+V{rz})}{(Vm-V_{rz})*(Vm+V{rz})}=[/latex] [latex]=frac{ frac{S}{2}*(Vm-V_{rz})frac{S}{2}*(Vm+V{rz})}{Vm^2-V_{rz}^2}=[/latex] [latex]=frac{ frac{S}{2}*2Vm}{Vm^2-V_{rz}^2}=frac{ S*Vm}{Vm^2-V_{rz}^2}=frac{ S}{frac{Vm^2-V_{rz}^2 }{Vm} }=[/latex] [latex]=frac{ S}{Vm-frac{V_{rz}^2 }{Vm} }[/latex] [latex]Pierwsza bedzie ta plynaca po jeziorze , ma wieksza predskosc.[/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.46.Dane:[/latex] [latex]V_1=130 frac{km}{h} [/latex] [latex]V_2=90 frac{km}{h} [/latex] [latex]V_{sr}= V_1-V_2=130 frac{km}{h}-90 frac{km}{h}=40 frac{km}{h}= frac{40*1000m}{3600s}=11,(1) frac{m}{s} [/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.47.Dane:[/latex] [latex]H=2m[/latex] [latex]x=15m[/latex] [latex]g=9,81 frac{m}{s^2} [/latex] [latex]a)[/latex] [latex]x= V_osqrt{ frac{2H}{g} } [/latex] [latex]V_o= frac{ x}{ sqrt{ frac{2H}{g}}}[/latex] [latex]V_o= frac{ x}{ sqrt{ frac{2H}{g}}}= frac{ 15m}{sqrt{ frac{2*2m}{9,81 frac{m}{s^2} }}}=23,5 frac{m}{s} [/latex] [latex]b)[/latex] [latex]Vk_1=V_o=23,5 frac{m}{s} [/latex] [latex]Vk_2=at= g* sqrt{ frac{2H}{g} }= sqrt{2Hg}= sqrt{2*2m*9,81 frac{m}{s^2} }=6,264 frac{m}{s} [/latex] [latex]tgalpha= frac{Vk_1}{Vk_2}= frac{23,5 frac{m}{s} }{6,6264 frac{m}{s}}=3,751486[/latex] [latex] alpha =75,0742^o[/latex] -------------------------------------------------------------------------------------------------------------------------- [latex]ZAD.48.Dane:[/latex] [latex]s_x=5cm=0,05m[/latex] [latex]V_o=30 frac{m}{s} [/latex] [latex]g=9,81 frac{m}{s^2} [/latex] [latex]S_w=V_o*t=V_o* sqrt{ frac{2S_x}{g}}=30 frac{m}{s}* sqrt{ frac{2*0,05m}{9,81 frac{m}{s^2}}}=3,028912664m[/latex]