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 1 kg moves with a speed of $12 \mathrm{~ms}^{-1}$ and the second part of mass 2 kg moves with $8 \mathrm{~ms}^{-1}$ speed. If the third part flies off with $4 \mathrm{~ms}^{-1}$ speed, then its mass is

Professor PC Thomas Classes · Answer

Momentum vectors: $\vec{p_1} = 12\hat{i}$, $\vec{p_2} = 16\hat{j}$. Total $p = \sqrt{12^2+16^2} = 20$. Third part $p_3 = 20 \Rightarrow 4m = 20 \Rightarrow m = 5$ kg.