Physics - Center of Mass Question with Solution | TestHub

For a perfectly inelastic collision, momentum is conserved, and the particles stick together. Let the final velocity of the combined mass $(m+2m)=3m$ be $\vec{V}=V_x\hat{i}+V_y\hat{j}$. Conservation of momentum in the x-direction:$m(2u)+2m(0)=(3m)V_x⟹2mu=3m{V}_x⟹V_x=\frac{2u}{3}$. Conservation of momentum in the y-direction:$m(0)+2m(u)=(3m)V_y⟹2mu=3m{V}_y⟹V_y=\frac{2u}{3}$. The final velocity vector is $\vec{V}=\frac{2u}{3}\hat{i}+\frac{2u}{3}\hat{j}$. The magnitude of the final velocity is $|\vec{V}|=\sqrt{V_x^2+V_y^2}=\sqrt{(\frac{2u}{3}{)}^2+(\frac{2u}{3}{)}^2}=\sqrt{2{\left(\frac{2u}{3}\right)}^2}=\frac{2u}{3}\sqrt{2}$.