An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right a...

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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass \( 1 \mathrm{~kg} \) moves with a speed of \( 12 \mathrm{~ms}^{-1} \) and the second part of mass \( 2 \mathrm{~kg} \) moves with \( 8 \mathrm{~ms}^{-1} \) speed. If the third part flies off with \( 4 \mathrm{~ms}^{-1} \) speed, then its mass is
(a) \( 3 \mathrm{~kg} \)
(b) \( 5 \mathrm{~kg} \)
(c) \( 7 \mathrm{~kg} \)
(d) \( 17 \mathrm{~kg} \)
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