A pigeon in flight experiences a force of air resistance given by $F=bv^2$, where v is the flight speed and b is constant. What is maximum speed of pigeon if its power output is P

Question

\[(a)\;2 \bigg(\frac{P}{b}\bigg)^{1/3} \quad (b)\;\bigg(\frac{P}{b}\bigg)^{1/3} \quad (c)\;\bigg(\frac{P}{b}\bigg)^{2/3} \quad (d)\;2 \bigg(\frac{P}{b}\bigg)^{2/3}\]