Question

A ball with a mass of `3 kg` is rolling at `16 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_r^'=-7.27" "m/s" The red ball's velocity after collision"`
`v_b^'=8.73" "m/s" The blue ball's velocity after collision"`

Explanation:

`"BEFORE COLLISION"`

`m_r=3" kg The red ball's mass"`
`v_r=16" "m/s " The velocity of red ball before collision"`

`P_r=m_r*v_r=16*3=48 kg*m/s`
`P_r:"(The red ball's momentum before collision)"`

`m_b=8" kg The blue ball's mass"`
`v_r=0" "m/s " The velocity of blue ball before collision"`

`P_b=m_b*v_b=8*0=0`
`P_b=0`

`P=P_r+P_b=48+0=48 kg*m/s`

`P:"(The Total momentum before collision)"`

`"AFTER COLLISION"`

`P_r^'=3*v_r^'" The red ball's momentum after collision"`
`P_b^'=8*v_b^' " The blue ball's momentum after collision"`
`P_^'=P_r^'+P_b^'`
`P^'=3*v_r^'+8*v_b^'`

`P^':"The total momentum after collision"`

`P=P^'" The conservation of momentum"`

`48=3*v_r^'+8*v_b^' " equation 1"`

`v_r+v_r^'=v_b+v_b^'" equation 2"`
`16+v_r^'=0+v_b^'`
`v_b^'=16+v_r^'" plug in equation 1"`

`48=3*v_r^'+8*(16+v_r^')`

`48=3v_r^'+128+8v_r^'`

`11v_r^'=48-128`

`11 v_r^'=-80`

`v_r^'=-80/11`

`v_r^'=-7.27" "m/s" The red ball's velocity after collision"`

`"So;"`
`v_b^'=16+v_r^'`

`v_b^'=16-7.27`

`v_b^'=8.73" "m/s" The blue ball's velocity after collision"`