An explosion blows a rock into three parts. Two parts go off at right angles to each other. Thes...

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, \( 1 \mathrm{~kg} \) first part moving with a velocity of \( 12 \mathrm{~m} \mathrm{~s}^{-1} \) and \( 2 \mathrm{~kg} \) second part moving with a velocity \( 8 \mathrm{~m} \mathrm{~s}^{-1} \). If the third part flies off with a velocity of \( 4 \mathrm{~m} \mathrm{~s}^{-1} \), its mass would be