Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed, then the ratio of the magnitude of impulses imparted to ball $a$ and ball $b$ by the wall along $X$ direction is:\\
(1) $1 : 1$\\
(2) $\sqrt{2} : 1$\\
(3) $2 : 1$\\
(4) $1 : \sqrt{2}$