Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially, $S_1$ is at rest and $S_2$ is moving with velocity $v$ along the $x$-axis. After the collision, $S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after the collision:

• A
  with a velocity of magnitude $\frac{m_2}{m_1} v \frac{\sqrt{5}}{2}$
• B
  with a velocity in the direction $\theta = \tan^{-1}\left(-\frac{1}{3}\right)$ to the $x$-axis
• C
  with a velocity whose direction makes an angle $\theta$ with the $x$-axis such that $\theta = \tan^{-1}\left(\frac{1}{2}\right)$ or $\theta = \tan^{-1}\left(-\frac{1}{2}\right)$
• D
  with a velocity of magnitude $\frac{m_1}{2m_2} v \sqrt{5}$