A smooth ball ‘A’ travels towards another identical ball ‘B’ with a velocity $u.$ Ball b is at rest and the impact parameter $d$ is equal to $\sqrt{3}R$ where $R$ is radius of each ball. Due to impact the direction of motion of ball A changes by ${30}^0.$ It is given that collision is elastic.

 

As collision is elastic and balls are identical the velocities of balls will be interchanged along  common normal direction. hence velocity of ball ‘A’ along common normal will be zero and  velocity of ball ‘B’ along common normal will be $u\cos \theta$ or $u\cos {60}^0$or $\frac{u}{2}.$

Along common tangent the velocities of the balls will not change

Hence ball ‘A’ will move in common tangent direction ( ${30}^0$ above x-axis) with speed $u\sin {60}^0$ or $\frac{u\sqrt{3}}{2}$ .