$7.(15$pts$)$ The uniform slender bar of mass $\backslash ($ m $\backslash )$ and length $\backslash ($ l $\backslash )$ has no angular velocity as end $\backslash ($ A $\backslash )$ strikes the ground against the stop with no rebound. Answer the following questions.

$($a$)(5$pts$)$ Draw a free body diagram and obtain the equations of motion of the bar. State the characteristics of the ground reaction forces $\backslash ($ R$\_\{$x$\},$ R$\_\{$y$\}\backslash )$ applied to the contact end $\backslash ($ A $\backslash )$ during and after collision, respectively.

$($b$)(5$pts$)$ Determine the linear impulse applied to the combined body during impact. Find the velocity of the center of mass right after collision. Determine the angular impulse applied to the combined body about the pivot point $\backslash ($ A $\backslash )$ during impact. Find the angular velocity of the combined body right after collision.

$($c$)(5$pts$)$ What is minimum magnitude of the initial velocity $\backslash ($ v$\_\{0\}\backslash )$ for which the bar will rotate about $\backslash ($ A $\backslash )$ to the vertical position?