#### Answer

(a) The tangential speed of the skaters is $4.67~m/s$ after they grab the rod.
(b) From the diagram, we can see that the direction of angular momentum is counterclockwise. Using the right hand rule, the direction of angular momentum is out of the screen.

#### Work Step by Step

(a) We can use conservation of angular momentum to find the final speed $v_f$:
$L_f= L_0$
$m_f~v_f~r = m_1~v_1~r+m_2~v_2~r$
$m_f~v_f = m_1~v_1+m_2~v_2$
$v_f = \frac{m_1~v_1+m_2~v_2}{m_f}$
$v_f = \frac{(60.0~kg)(6.0~m/s)+(30.0~kg)(2.0~m/s)}{60.0~kg+30.0~kg}$
$v_f = 4.67~m/s$
The tangential speed of the skaters is $4.67~m/s$ after they grab the rod.
(b) By conservation of angular momentum, the direction of angular momentum is the same before and after the skaters grab the rods. From the diagram, we can see that the direction of angular momentum is counterclockwise. Using the right hand rule, the direction of angular momentum is out of the screen.