One ice skater of mass $m$ moves with speed $2v$ to the right,while another of the same mass $m$ moves with speed $v$ toward the left,as shown in figure $I$. Their paths are separated by a distance $b$. At $t = 0$,when they are both at $x = 0$,they grasp a pole of length $b$ and negligible mass. For $t > 0$,consider the system as a rigid body of two masses $m$ separated by distance $b$,as shown in figure $II$. Which of the following is the correct formula for the motion after $t = 0$ of the skater initially at $y = b/2$?

• A
  $x = 2vt, y = b/2$
• B
  $x = vt + 0.5b \sin(3vt/b), y = 0.5b \cos(3vt/b)$
• C
  $x = 0.5vt + 0.5b \sin(3vt/b), y = 0.5b \cos(3vt/b)$
• D
  $x = 0.5vt + 0.5b \sin(6vt/b), y = 0.5b \cos(6vt/b)$