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) $\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})$

Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in figure. They collide completely inelastic and move as a single particle $C$. The angle $\theta$ that the path of $C$ makes with the $X$-axis is given by-
(1) $\tan \theta = \frac { \sqrt { 3 } - \sqrt { 2 } } { 1 - \sqrt { 2 } }$
(2) $\tan \theta = \frac { 1 - \sqrt { 2 } } { \sqrt { 2 } ( 1 + \sqrt { 3 } ) }$
(3) $\tan \theta = \frac { 1 - \sqrt { 3 } } { 1 + \sqrt { 2 } }$
(4) $\tan \theta = \frac { \sqrt { 3 } + \sqrt { 2 } } { 1 - \sqrt { 2 } }$

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.