Question

A ball with a mass of `5 kg` is rolling at `3 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^'=1/3 m/s`
`v_2^'=10/3 m/s`

Explanation:

`"momentum before collision=momentum after collision"`
`m_1=3 kg; v_1=3 m/s; m_2=4 kg; v_2=0`
`P_b=m_1*v_1+m_2*v_2=5*3+4*0`
`P_b=15 "(momentum before collision)"`
`P_a=m_1*V_1^'+m_2*V_2'"(momentum after collision)"`
`P_a=5*V_1^'+4*V_2^'`
`P_b=P_a`
`15=5*V_1^'+4*V_2^'`; `equation 1`
`v_1+v_1^'=v_2+v_2^'`
`3+v_1^'=0+v_2^'`;`equation 2`
write `3+v_1^'` instead `v_2^'` in equation 1
`15=5*v_1^'+4*(3+v_1^')`
`15=5*v_1^'+12+4*v_1^'`
`15-12=9*v_1^'`
`3=9*v_1^'`
`v_1^'=1/3 m/s`
`"now use equation 2"`
`3+v_1^'=v_2^'`
`3+1/3=v_2^'`
`v_2^'=10/3 m/s`