Two hockey players $($each with mass $\backslash (=80\backslash$mathrm$\{$~kg$\}\backslash ))$ collide mid$-$ice and get tangled together. Initially, player $1$ is travelling at $\backslash (2\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ towards the home team goal having just left the bench at a $45$ deg angle relative to the long axis $($ y axis on figure$)$ of the ice. Player $2$ is traveling at $\backslash (4\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ along the long axis of the ice towards the opposition goal. After the collision how fast and in what direction relative to the long axis of ice will the two players be moving together. $($Assume ice is frictionless surface; long axis $=$ y axis. $)$