$[0/1$ Points$]$

A $25\mathrm{.}7-kg$ boy stands on the edge of a merry$-$go$-$round of mass $147.kg$ and radius $2\mathrm{.}52$ m which is at rest. The moment of inertia of the merry$-$go$-$round about its axis of rotation is $264kg**m^2.$ The boy catches a ball of mass $1\mathrm{.}85$ kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity of $12\mathrm{.}0\frac{m}{s}$ that makes an angle of $=37\mathrm{.}0$ with a line tangent to the outer edge of the merry$-$go$-$round, as shown in the overhead view of the figure below. What is the angular speed. of$.$ the merry$-$go$-$round just after that ball is caught?

rad$/$s