A body is projected with a velocity of  $60 m{s}^{-1 }$at  ${30}^0$ to horizontal.

	COLUMN-I		COLUMN-II
I	Initial velocity vector	P	$60\sqrt{3}\stackrel{\wedge }{i}+40\stackrel{\wedge }{j}$
II	Velocity after 3 s	Q	$30\sqrt{3}\stackrel{\wedge }{i}+10\stackrel{\wedge }{j}$
III	Displacement after 2 s	R	$30\sqrt{3}\stackrel{\wedge }{i}+30\stackrel{\wedge }{j}$
IV	Velocity after 2 s	S	$30\sqrt{3}\stackrel{\wedge }{i}$
		T	$30\sqrt{3}\stackrel{\wedge }{j}$

 $$\begin{gathered} I\to R;II\to S;III\to P;IV\to Q \\ \overline{U}=u\cos \theta \stackrel{\wedge }{i}+u\sin \theta \stackrel{\wedge }{j} \\ \overline{U}=60\frac{\sqrt{3}}{2}\stackrel{\wedge }{i}+60\left(\frac{1}{2}\right)\stackrel{\wedge }{j} \\ \overline{U}=30\sqrt{3}\stackrel{\wedge }{i}+30\stackrel{\wedge }{j} \end{gathered}$$
Velocity after 3S
 $$\begin{gathered} \overline{V}=u\cos \theta \stackrel{\wedge }{i}+(u\sin \theta -gt)\stackrel{\wedge }{i} \\ \overline{V}=30\sqrt{3}\stackrel{\wedge }{i}(30-10\text{x}3)\stackrel{\wedge }{i} \\ \therefore \overline{V}=30\sqrt{3}\stackrel{\wedge }{i} \end{gathered}$$
Displacement after 2S 
 $$\begin{gathered} \overline{S}=u\cos \theta \stackrel{\wedge }{i}+(u\sin \theta t-\frac{1}{2}g{t}^2)\stackrel{\wedge }{j} \\ \overline{S}=30\sqrt{3}\text{x2}\stackrel{\wedge }{i}+\left(30\text{x2-}\frac{1}{2}{\text{x10(2)}}^2\right)\stackrel{\wedge }{j} \\ \therefore \overline{S}=60\sqrt{3}\stackrel{\wedge }{i}+40\stackrel{\wedge }{j} \end{gathered}$$
Velocity after 2S
 $$\begin{gathered} \overline{V}=u\cos \theta \stackrel{\wedge }{i}+(u\sin \theta -g{t}^2)\stackrel{\wedge }{j} \\ \overline{V}=30\sqrt{3}\stackrel{\wedge }{i}+(30-\text{10x2})\stackrel{\wedge }{j} \\ \overline{V}=30\sqrt{3}\stackrel{\wedge }{i}+10\stackrel{\wedge }{j} \end{gathered}$$