A rocket is fired vertically from a launch pad $B$. Its flight is tracked by radar from point $A$. Determine the velocity of the rocket in terms of $b$, $\theta$, and $d\theta/dt$.

A. $v = b \cos \theta$
B. $v = b \cos^2 \theta$
C. $v = b \cos^2 \theta \dot\theta$
D. $v = b \sec \theta$
E. $v = b \sec \theta \dot\theta$
F. $v = b \sec^2 \theta \dot\theta$