Question

A ball with a mass of `6 kg` is rolling at `6 m/s` and elastically collides with a resting ball with a mass of `8 kg`. What are the post-collision velocities of the balls?

Answer 1

`v_1^'=-6/7 " "m/s`

`v_2^'=36/7 " "m/s`

Explanation:

`m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'`
`6*6+8*0=6*v_1^' + 8*v_2^'`
`36+0=6*v_1^'+8*v_2^'`
`36=6*v_1^'+8*v_2^'" "(1)`

`" we use the equation " v_1+v_1^'=v_2+v_2^'`
`" for calculating velocities after collision"`

`6+v_1^'=0+v_2^'`
`6+v_1^'=v_2^'" "(2)`

`36=6*v_1^'+8(6+v_1^')`
`36=6*v_1^'+48+8*v_1^'`
`36-48=14*v_1^'`
`-12=14*v_1^'`
`v_1^'=-12/14=-6/7 " "m/s`

`"use (2)"`
`6-6/7=v_2^'`
`(42-6)/7=v_2^'`

`v_2^'=36/7" " m/s`