Give answers and explain working $.$ Two particles collide with a normal direction defined: $0\mathrm{.}2$i$+0\mathrm{.}98$j $($eT$=0\mathrm{.}98$i$+-0\mathrm{.}2$j$).$ The first mass has a mass of $5$ kg and a velocity of $5$i m$/$s$.$ The second mass has a mass of $4$ kg and a velocity of $-2$i$+2$j m$/$s$.$ The collision has a coefficient of restitution of $0\mathrm{.}2.$

$1.$ Determine the tangential velocity of the first particle after the impact $[$m$/$s$].$

$2.$Determine the velocity in the normal direction of the first particle after the impact $[$m$/$s$].($eN w$.$r$.$t$.$ the collision framework, not the kinematic reference frame system$)$

$3.$ Determine the velocity in the i$-$direction of the first particle after the impact $[$m$/$s$].$