Problem $17$:$046-$ The pin velocity of a falling two$-$rod composite system

The uniform rods $AB$ and $BC$ weigh $2\mathrm{.}500$ kg and $4\mathrm{.}200$ kg $,$ respectively, and the small wheel at $C$ is of negligible mass. Knowing that in the position shown the velocity of wheel $C$ is $2\mathrm{.}500\frac{m}{s}$ to the right, determine the velocity of pin $B$ after rod $AB$ has rotated through $90.($Round the final answer to three decimal places.$)$

The velocity of pin $B$ after rod $AB$ has rotated through $90$ is: $7$n$!$