Problem $7($Halliday Problem $11\mathrm{.}63)$

In Fig. $11-56,$ a $30$ kg child stands on the edge of a stationary merry$-$go$-$round of radius $2\mathrm{.}0$ m $.$ The rotational inertia of the merry$-$go$-$round about its rotation axis is $150kg*m^2.$ The child catches a ball of mass $1\mathrm{.}0$ kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity vec$(v)$ of magnitude $12\frac{m}{s},$ at angle $=37$ with a line tangent to the outer edge of the merry$-$go$-$round, as shown. What is the angular speed of the merry$-$go$-$round just after the ball is caught?