$$A $2\mathrm{.}20$ kg hoop $1\mathrm{.}20$ m in diameter is rolling to the right without slipping on a horizontal floor at a steady $($a$)$ How fast is its center moving? $($b$)$ What is the total kinetic energy of the hoop? $($c$)$ Find the velocity vector of each of the following points, as viewed by a person at rest on the ground: $($i$)$ the highest point on the hoop; $($ii$)$ the lowest point on the hoop; $($iii$)$ a point on the right side of the hoop, midway between the top and the bottom. $($d$)$ Find the velocity vector for each of the points in part $($c$),$ but this time as viewed by someone moving along with the same velocity as the hoop.