# 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

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

$Power = F \times V$
$P=bv^2 \times V$
$\quad=bv^3$
$v=\bigg(\large\frac{P}{b}\bigg)^{1/3}$
Hence b is the correct answer.

edited Feb 10, 2014 by meena.p