Hail is formed when ice particles from the upper layers of a thunderstorm fall through the rain, pick up a layer of water, and then get caught in the updraft of the storm which freezes the accumulated water. This process repeats itself until the weight of the hailstone is too large to be supported by the aerodynamic drag generated by the updraft. Estimate the velocity, \(v_{\infty}\), of the updraft required to make a hailstone \(3 \mathrm{~cm}\) in diameter. Assume air properties that exist at about \(7000 \mathrm{~m}\) where the temperature is \(-30.5^{\circ} \mathrm{C}\).

\[ho_{\text {air }}=0.59 \frac{\mathrm{kg}}{\mathrm{m}^{3}} \quad \mu_{\text {air }}=1.56 \times 10^{-5} \frac{\mathrm{Ns}}{\mathrm{m}^{2}} \quad g=9.785 \frac{\mathrm{m}}{\mathrm{s}^{2}} \quad ho_{\text {ice }}=948 \frac{\mathrm{kg}}{\mathrm{m}^{3}}\]