Question

5.0-kg ball is moving at 3.2 m/s when it strikes a 3.6-kg ball moving 2.7m/s. They are both headed in the same direction. After the collision the 5.0kg ball moves at 1.5m/s, what is the velocity of the 3.6kg ball after the collision?

Answer 1

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,

`\begin{gathered} Mu_1+mu_2=Mv_1+mv_2 \\ \Rightarrow mv_2=Mu_1+mu_2-Mv_1 \\ v_2=(Mu_1+mu_2-Mv_1)/(m) \end{gathered}`

Where v₂ is the velocity of the 3.6 kg ball after the collision.

On substituting the known values,

`\begin{gathered} v_2=(5.0*3.2+3.6*2.7-5.0*1.5)/(3.6) \\ =(16+9.72-7.5)/(3.6) \\ =5.06\text{ m/s} \end{gathered}`

Therefore the velocity of the 3.6 kg ball after the collision is 5.06 m/s