Given,
The mass of the 1st ball, M=5.0 kg
The mass of the 2nd ball. m=3.6 kg
The initial velocity of the 1st ball, u₁=3.2 m/s
The initial velocity of the second ball, u₂=2.7 m/s
The speed of the 1st ball after the collision, v₁=1.5 m/s
From the law of conservation of momentum, the total momentum of a system always remains constant. That is the total momentum of the balls before and after the collision is the same.
Thus,
[tex]\begin{gathered} Mu_1+mu_2=Mv_1+mv_2 \\ \Rightarrow mv_2=Mu_1+mu_2-Mv_1 \\ v_2=\frac{Mu_1+mu_2-Mv_1}{m} \end{gathered}[/tex]Where v₂ is the velocity of the 3.6 kg ball after the collision.
On substituting the known values,
[tex]\begin{gathered} v_2=\frac{5.0\times3.2+3.6\times2.7-5.0\times1.5}{3.6} \\ =\frac{16+9.72-7.5}{3.6} \\ =5.06\text{ m/s} \end{gathered}[/tex]Therefore the velocity of the 3.6 kg ball after the collision is 5.06 m/s
