Question

A ball with a mass of `3 kg` is rolling at `1 m/s` and elastically collides with a resting ball with a mass of `4 kg`. What are the post-collision velocities of the balls?

Answer 1

`v_1^'=-1/7 m/s`
`v_2^'=6/7m/s`

Explanation:

`m_1*v_1+m_2v_2=m_1v_1^'+m_2v_2^'" "(1)`
`"total momentum before collision=total momentum after collision"`
`1/2*m_1*v_1^2+1/2*m_2*v_2^2=1/2.m_1*v_1'^2+1/2*m_2*v_2'^2`

`m_1*v_1^2+m_2*v_2^2=m_1*v_1'^2+m_2*v_2'^2" "(2)`
`"we obtain the equation of (3),if we arrange (1) and (2)"`
`v_1+v_1^'=v_2+v_2^' " "(3)`
`3*1+4*0=3*v_1^'+4*v_2^'`
`3=3*v_1^'+4*v_2^'" "(4)`
`"use (3)"`
`1+v_1^'=0+v_2^'`
`v_2^'=1+v_1^'" "(5)`
`"use (4)"`
`3=3*v_1^'+4(1+v_1^')`
`3=3*v_1^'+4+4v_1^'`
`-1=7v_1^'" "v_1^'=-1/7 m/s`
`"use (5)"`
`v_2^'=1-1/7`
`v_2^'=6/7m/s`