Question

A ball with a mass of `5 kg` is rolling at `18 m/s` and elastically collides with a resting ball with a mass of `3 kg`. What are the post-collision velocities of the balls?

Answer 1

Given

Mass of 1st ball `m_1=5` kg

Mass of 2nd ball `m_2=3` kg

Initial velocity of 1st ball `u_1=18m"/"s`

Initial velocity of 2nd ball `u_2=0m"/"s`

Let post collision velocity of 1st ball be `v_1` and that of 2nd ball be `v_2`

By conservation of momentum

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

`5*18+3*0=5v_1+3v_2`

`=>5v_1+3v_2=90.....[1]`

Again the collision being elastic one the relative velocity of one ball with respect to the other is reversed by the collision and we get

`v_2-v_1=u_1-u_2`

`=>v_2-v_1=18-0`

`=>v_2-v_1=18.......[2]`

By [1] and [2] we get

`5v_1+3(18+v_1)=90`

`=>8v_1=90-54=36`

`=>v_1=36/8=4.5` m/s

`v_2=18+v_1=18+4.5=22.5`m/s