Z zasady zachowania energii możemy napisac: [latex]E_{poczatkowa}=E_{koncowa}\ frac{mv^2}{2}=mgh\v^2=2gh\h= frac{v^2}{2g}= frac{100}{20}=5m\ [/latex] Ze wzoru na drogę przebytą w czasie: [latex]s=V_ot- frac{gt^2}{2}\ 5=10t- frac{10}{2}t^2\5=10t-5t^2\5t^2-10t+5=0\t^2-2t+1=0 \(t-1)^2=0\t=1[/latex]
[latex]v_{o} = 10frac{m}{s}\g = 10frac{m}{s^{2}}\szukane:\t_{w} = ?\h = ?[/latex] [latex]t_{w} = frac{v_{o}}{g} = frac{10m/s}{10m/s^{2}}=1 s[/latex] [latex]E_{p} = E_{k}\\mgh = frac{mv_{o}^{2}}{2} |*frac{2}{m}\\2gh = v_{o}^{2} /:2g\\h = frac{v_{o}^{2}}{2g} = frac{(10m/s)^{2}}{2*10m/s^{2}} = frac{100}{20} m = 5 m[/latex]
