Question

A ball with a mass of `6 kg` is rolling at `25 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^'=125/7 m/s`
`v_2^'=300/7 m/s`

Explanation:

`vec P_1+vec P_2:" total momentum before collision "`
`vec P_1^'+vec P_2^':" total momentum after collision"`
`vec P_1+vec P_2=vec P_1^'+vec P_2^'" conservation of momentum"`

`m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'`
`6*25+1*0=6*v_1^'+1*v_2^'`
`150=6*v_1^'+1*v_2^'" (1)"`

`v_1+v_1^'=v_2+v_2^'" (2)"`
`25+v_1^'=0+v_2^'`
`v_2^'=25+v_1^'" (3)"`

`"let's use (1)"`
`150=6*v_1^'+25+v_1^'`
`150-25=7v_1^'`
`125=7v_1^'`
`v_1^'=125/7 m/s`

`"let's use (3)"`
`v_2^'=25+125/7`
`v_2^'=(175+125)/7`
`v_2^'=300/7 m/s`