1Consider the system of 4 balls to be acting on the COM.
Momentum conservation equation along z-axis:---
mv = 4m*v1 - m*v2 ---- (i)
As, the travelling ball will return by the same path due to symmmetry.
e = velocity of separation/velocity of approach
1 = (v1+v2)/v
v = v1+v2 ---- (ii)
Solving 1 & 2
we get,
v2 = 3v/5;
Now apply energy conservation equation before and after collision, as it is elastic collision
energy will be conserved.
consider, speed of 4 similar balls = v3
0.5mv^2 = 0.5*4m*(v3)^2 + 0.5 *m*((3/5)v)^2
m*(16/25)*v^2 = 4m*(v3)^2
v3 = 2v/5;