A 30.0-kg object has a drag force with a magnitude proportional to the square of its speed. The object falls with an acceleration 4.00 m/s2 downward when it is falling downward at 70.0 m/s. What is its terminal velocity?

At terminal velocity , the drag force has the same magnitude as the object's weight since the object is in equilibrium:

Drag is proportional to the square of the speed, so there is some constant k such that

and in particular, at terminal velocity we have

At the moment the object is falling with speed v = 70.0 m/s and with acceleration a = 4.00 m/s², the net force on it is

Solve for k :

Now solve for the terminal velocity: