Marinada '23

[lang=hr] U prvom kvadrantu koordinatnog sustava se nalazi dvodimenzionalnog spremnik horizontalne duljine $2\, m$ i visine $1\,m$ u donjem lijevom kutu spremnika(neka se donji lijevi kut nalazi u točki $(0,0)$) nalazi se $5$ jako malenih čestica od kojih svaka u trenutku $t=0$ ima nasumičan vektor smjera određen preko nasumično odabrane točke iz ravnine i točke $(0,0)$ tako da je brzina iz $[0,4] \, ms^{-1}$ i kut između $[0,\frac{\pi} {2}]$. \\ Spremnik je podijeljen s dva vertikalna pravca $x=0.8$ i $x=1.2$. \\ Kolika je vjerojatnost da se svih pet čestica nalaze između ova dva pravca nakon $1$ sekunde? \\ Pretpostavite da su čestice toliko malene da se ne mogu međusobno sudarati. [/lang] [lang=en] In the first quadrant of the coordinate system, there is a two-dimensional container of horizontal length $2\, m$ and height of $1\,m$. In the left bottom part of the container (let that be point $(0,0)$) there are $5$ extremely small particles, each of which in time $t=0$ has a random direction vector determined with a random point from the plane and with point $(0,0)$ such that the velocity is between $[0,4] \, ms^{-1}$ and the angle is between $[0,\frac{\pi} {2}]]$. \\ The container is divided into two parts by vertical lines $x=0.8$ and $x=1.2$. \\ What's the probability that all five particles find themselves between those two lines after $1$ second? \\ You may suppose that particles are so small that they cannot collide one with another. [/lang]