Question

A ball with a mass of `14kg` moving at `1 m/s` hits a still ball with a mass of `15 kg`. If the first ball stops moving, how fast is the second ball moving?

Answer 1

`v_1^'=-1/29 m/s`

`v_2^'=28/29 m/s`

Explanation:

`"we must use the conservation of momentum"`
`sum P_"before"=sum P_"after"`
`"the total momentum before collision must be equal the total"`
`"momentum after collision."`
`m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'`
`14*1+15*0=14*v_1^'+15*v_2^'`

`14+0=14*v_1^'+15*v_2^'`

`14=14*v_1^'+15*v_2^'" (1)"`

`v_1+v_1^'=v_2+v_2^'`

`1+v_1^'=0+v_2^'`

`v_2^'=color(green)(1+v_1^')" (2)"`

`"use (1)"`

`14=14*v_1^'+15*(color(green)(1+v_1^'))`

`14=14*v_1^'+15+15*v_1^'`

`14-15=29*v_2^1`

`-1=29*v_1^'`

`v_1^'=-1/29 m/s`

`"use (2)"`

`v_2^'=1-1/29`

`v_2^'=(29-1)/29`

`v_2^'=28/29 m/s`