Question

A ball with a mass of `2 kg` is rolling at `6 m/s` and elastically collides with a resting ball with a mass of `1 kg`. What are the post-collision velocities of the balls?

Answer 1

`v_1^'=2 m/s`
`v_2^'=8 m/s`

Explanation:

`vec P_1 + vec P_2= vec P_2^' + vec P_2^'" the conservation of momentum"`
`m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'`
`2*6+0=2*v_1^'+1*v_2^'`
`12=2*v_1^'+v_2^'" (1)"`
`v_1+v_1^'=v_2+v_2^'" (2)`
`6+v_1^'=0+v_2^'`
`v_2^'=6+v_1^'" (3)"`
`"use equation (1)"`
`12=2*v_1^'+6+v_1^'`
`12-6=3*v_1^2`
`6=3*v_1^' " " v_1^'=2 m/s`
`"use equation (3)"`
`v_2^'=6+2`
`v_2^'=8 m/s`