An explosion breaks a $27\mathrm{.}0-$kg object initially at rest into three parts. Part $(1)$ has a mass$\mathrm{}{\mathrm{ m}}_1=3\mathrm{.}60-$kg and a velocity of $50\mathrm{.}0\frac{}{}$ m/s due west. Part $(2)$ has a mass m ${}_2=4\mathrm{.}70-$kg and a velocity of $68\mathrm{.}0\frac{}{}$ m/s due south. What is the magnitude of the velocity of part $(3)?$