[tex]d_1=\frac{g(t+\tau)^2}{2}=\frac{g\tau^2+gt^2+2gt\tau}{2}\\ d_2=\frac{gt^2}{2}\\ d=d_1-d_2=\frac{g\tau^2+gt^2+2gt\tau}{2}-\frac{gt^2}{2}=\frac{g\tau^2+2gt\tau}{2}<=>0,5=\frac{10\tau^2+20\tau}{2}<=>1=10\tau^2+20\tau[/tex]
[tex]10\tau^2+20\tau-1=0\\\Delta=20^2+4*10*1=400+40=440\\\tau_{1,2}=\frac{-20\pm\sqrt{440}}{2*10}=\frac{-20\pm20,97}{20}\\ \tau_1=\frac{-20+20,97}{20}= 0,048 s\\\tau_2=\frac{-20-20,97}{20}<0=>\tau_2-N.C.\\\tau=0,048 s[/tex]
