# motion under gravity

mass*acceleration= force and here the force is gravity, downward, -mg and friction, $-\gamma v^3$ (- because the force is always opposing the motion).
$m\frac{dv}{dt}= -mg- \gamma v^3$. The "terminal velocity" is when dv/dt= 0.
To find the "equation of motion" solve that equation for v and then solve $\frac{dx}{dt}= v$ to get the height as a function of t.