A ball A is falling vertically downwards with velocity $v_1$. It strikes elastically a wedge moving horizontally with velocity $v_2$ as shown in figure.

The ratio  $\frac{v_2}{v_1}$, so that the ball bounces back vertically upwards relative to the wedge is $\sqrt{K}$ then $K$ is  

In the figure let ${{\overrightarrow{v}}_{12}}^1=$ velocity of ball w.r.t wedge before collision and ${\overrightarrow{v}}_{12}=$ velocity of ball w.r.t wedge after collision, which must be in vertically upward direction as shown

In elastic collision ${\overrightarrow{v}}_{12}$ and ${\overrightarrow{v}}_{12}$ will make equal angle $\left(say\alpha \right)$ with the normal to the plane.
We can show that  $\alpha ={30}^o$
 $\Rightarrow \angle MON={30}^o$
Now,   $\frac{v_2}{v_1}=\cot {30}^o=\sqrt{3}$