Perfectly Inelastic Collision – Final Velocity

Questions where particles collide and stick together, and the task is to find the final velocity (magnitude or direction) of the combined mass.

jee-main 2014 Q5 View
Three masses $\mathrm{m}$, $2\mathrm{m}$ and $3\mathrm{m}$ are moving in $\mathrm{x}$-$\mathrm{y}$ plane with speed $3\mathrm{u}$, $2\mathrm{u}$ and $\mathrm{u}$ respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be:
(1) $\frac{u}{12}(\hat{i}+\sqrt{3}\hat{j})$
(2) $\frac{u}{12}(\hat{i}-\sqrt{3}\hat{j})$
(3) $\frac{u}{12}(-\hat{i}+\sqrt{3}\hat{j})$
(4) $\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})$
jee-main 2022 Q23 View
A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then the trolly car starts moving with velocity $2\mathrm{~m\,s^{-1}}$. The velocity of the running man was $\_\_\_\_$ $\mathrm{m\,s^{-1}}$, when he jumps into the car.