In outer space, far from other objects, a small block of mass m $=3$ kg traveling at speed

v$1=10$ m$/$s approaches an object initially at rest that consists of two small spheres each of

mass M $=20$ kg connected by a low$-$mass rod, with center$-$to$-$center distance d $=0\mathrm{.}40$ m$.$

The block is observed to bounce off the upper sphere and proceed with speed v$2=8$ m$/$s at

an angle $0=30$ to the original direction.

$($a$)$ Find the velocity of the center of the rod after the collision, $=$ vxi $+$ Vyj$.$

$($b$)$ Just before the collision, what is the vector angular momentum of the block with respect to

point A$,$ the center of the rod?

$($c$)$ Just after the collision, what is the vector angular momentum of the block with respect to

point A$,$ the center of the rod?

$($d$)$ Find the angular speed w of the rod after the collision.