Answer
Final Speed of ball 2 is $v = 6.93 ms^{-1}$.
Work Step by Step
The diagram below shows the situation as the incident ball (the left-most ball) makes contact with the other two and it exerts an impulse of the same magnitude on each ball, along the line that joins the centers of the incident ball and the target ball. The target balls leave the collision along those lines, while the incident ball leaves the collision along the x axis. The three dashed lines that join the centers of the balls in contact form an equilateral triangle, so both of the angles marked $θ= 30^{\circ} $.
Let ν = 0 be the velocity of the incident ball before the collision and V be its velocity afterward. The two target balls leave the collision with the same speed. Let v represent that speed. Each ball has mass m. Since the x component of the total momentum of the three-ball system is conserved,
=mV+3mνcosθ
and since the total kinetic energy is conserved .
Solution is attached below :
