a ball moving with a speed 9m/s strikes an identical ball at rest , such that after the collisoins, the direction of each ball makes an angle of 30 degree with original line of motion.. find the speed of two balls after collisins

Let the mass of the balls be ‘m’.

Before collision net momentum along X axis is = 9m

Before momentum net momentum along Y axis is = 0

After collision, let the velocities of the balls be v₁ and v₂.

So, after collision the momentum along X axis is = mv₁ cos30 + mv₂ cos30

And the momentum along Y axis is = mv₁ sin30 - mv₂ sin30

Now, applying law of conservation of momentum,

mv₁ cos30 + mv₂ cos30 = 9m

=> v₁ + v₂ = 9/(cos30) = 10.39 ………..(1)

And,

mv₁ sin30 - mv₂ sin30 = 0

=> v₁ = v₂ …………(2)

Using, (1) and (2),

v₁ = v₂ = 10.39/2 ≈ 5.2 m/s