A playground merry$-$go$-$round has radius $2\mathrm{.}4$ m and rotational inertia $2100$ kg$$m$2$ about a

vertical axis through its center. The merry$-$go$-$round turns with negligible friction. A child

applies an $18$ N force tangentially to the edge of the merry$-$go$-$round for $15$ s$.$ If the

merry$-$go$-$round is initially at rest:

a$)$ What is its angular velocity after the $15$ s interval?

b$)$ How much work did the child do on the merry$-$go$-$round?

c$)$ What is the average power supplied by the child