$A$ ball is thrown upward with an initial velocity $V_0$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m \gamma v^2$ (where $m$ is the mass of the ball,$v$ is its instantaneous velocity,and $\gamma$ is a constant). The time taken by the ball to rise to its zenith is:

• A
  $\frac{1}{\sqrt{\gamma g}} \tan^{-1} \left( \sqrt{\frac{\gamma}{g}} V_0 \right)$
• B
  $\frac{1}{\sqrt{\gamma g}} \ln \left( 1 + \sqrt{\frac{\gamma}{g}} V_0 \right)$
• C
  $\frac{1}{\sqrt{\gamma g}} \sin^{-1} \left( \sqrt{\frac{\gamma}{g}} V_0 \right)$
• D
  $\frac{1}{\sqrt{2 \gamma g}} \tan^{-1} \left( \sqrt{\frac{2 \gamma}{g}} V_0 \right)$