Question

A ball with a mass of `5 kg` is rolling at `8 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^'=8/9 " "m/s`

`v_2^'=80/9" "m/s`

Explanation:

`m_1=5" "kg`
`v_1=8" "m/s`
`P_1=m_1*v_1=5*8=40" " kg*m/s`

`m_2=4" "kg`
`v_2=0`
`P_2=m_2*v_2=4*0=0`

`Sigma P_b=P_1+P_2" total momentum"`
`Sigma P_b=40+0=40" "kg*m/s`

`"post collision velocities :"`

`v_1^'=(2*Sigma P_b)/(m_1+m_2)-v_1`

`v_1^'=(2*40)/(5+4)-8`

`v_1^'=80/9-8`

`v_1^'=(80-72)/9`

`v_1^'=8/9 " "m/s`

`v_2^'=(2*Sigma P_b)/(m_1+m_2)-v_2`

`v_2^'=(2*40)/(5+4)-0`

`v_2^'=80/9" "m/s`