Three forces act significantly on a freely floating heliumfilled balloon: gravity, air resistance (or drag force), and a buoyant force. Consider a spherical helium-filled balloon of radius r=15 cm rising upward through 0⁰C air and m = 2.6 g is the mass of the (deflated) balloon itself. For all speeds v, except the very slowest ones, the flow of air past a rising balloon is turbulent, and the drag force FD is given by the relation
FD=1/2CDrhoairπr²v².
where the constant CD = 0.47 is the "drag coefficient" for a smooth sphere of radius r. If this balloon is released from rest, it will accelerate very quickly (in a few tenths of a second) to its terminal velocity vT, where the buoyant force is cancelled by the drag force and the balloon's total weight.

Assuming the balloon's acceleration takes place over a negligible time and distance, how long does it take the released balloon to rise a distance h = 15 m ?