In a playground there is a small merry$-$go$-$round of radius $1\mathrm{.}24$ m and mass $168$ kg $.$ The radius of gyration is $0\mathrm{.}946$

m$.$ A child of mass $47\mathrm{.}1$ kg runs at a speed of $3\mathrm{.}58$m$//$s tangent to the rim of the merry$-$go$-$round while it is at rest, and then jumps on$.$ Find the angular velocity $($in radians$/$second$)$ of the merry$-$go$-$round and child together. Neglect friction.