Question

A ball with a mass of `6 kg` is rolling at `7 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^'=-7 m/s`
`v_2^'=0`

Explanation:

`"total momentums before event=total momentum after event"`
`vec P_(1b)+ vec P_(2b)=vec P_(1a)+ vec P_(2a)`
`6*7+0=6*v_1^'+8*v_2^'`
`42=6*v_1^'+8*v_2^' " (1)"`
`v_1+v_1^'=v_2+v_2^'`
`7+v_1^'=0+v_2^' " (2)"`
`v_1^'=v_2^'-7`
`42=6*(v_2^'-7)+8.v_2^'`
`42=6*v_2^'-42+8*v_2^'`
`14*v_2^'=0`
`v_2^'=0`
`v_1^'=0-7`
`v_1^'=-7 m/s`