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

Question

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 2 kg moves with a speed of $3 \mathrm{~m} \mathrm{s}^{-1}$ and the second part of mass 1 kg moves with $8 \mathrm{~m} \mathrm{s}^{-1}$ speed. If the third part flies off with $5 \mathrm{~m} \mathrm{s}^{-1}$ speed, then its mass is

Professor PC Thomas Classes · Answer

Initial momentum is zero. $\vec{p}_3 = -(\vec{p}_1 + \vec{p}_2)$. Since they are at right angles, magnitude $p_3 = \sqrt{p_1^2 + p_2^2}$. $p_1 = 2 	imes 3 = 6 \mathrm{~kg~m/s}$, $p_2 = 1 	imes 8 = 8 \mathrm{~kg~m/s}$. So $p_3 = \sqrt{6^2 + 8^2} = 10 \mathrm{~kg~m/s}$. Given $v_3 = 5 \mathrm{~m/s}$, mass $m_3 = p_3 / v_3 = 10 / 5 = 2 \mathrm{~kg}$.