A $27\mathrm{.}4$ kg dog $($Astro$?)$ is running northward at $2\mathrm{.}60$ m$/$s$,$ while a $4\mathrm{.}50$ kg cat $($Simba$?)$ is

running eastward at $3\mathrm{.}12$ m$/$s$.$ Their $77\mathrm{.}0$ kg owner has the same momentum as the two pets

taken together. Find the direction and magnitude of the owner$$s velocity.