A ball is thrown upward with an initial velocity V _ 0 from the...

Net force on ball,
$F = - mg - m\gamma{v}^{2}$
$a = - g - \gamma{v}^{2}$
$\dfrac{dv}{dt} = - g - \gamma{v}^{2}$
$\mathop{∫}_{v = {V}_{0}}^{v = 0}\dfrac{dv}{g + \gamma{v}^{2}} =\mathop{∫}_{t = 0}^{t}- dt$
${\left(\dfrac{1}{\sqrt{g\gamma}}\tan^{- 1}\sqrt{\dfrac{\gamma}{g}}v\right)}_{v = {V}_{0}}^{v = 0} = - t$
$∴ t = \dfrac{1}{\sqrt{\gammag}}\tan^{- 1}\left(\sqrt{\dfrac{\gamma}{g}}{V}_{0}\right)$