A 10kg ball and 20kg ball approach each other with velocities `20ms^(-1)` and `10ms^(-1)` respectively. What are their velocities after collision if the collision is perfectly elastic?

Explanation

`m_(1)=10kg,m_(2)=20kg`
`u_(1)=20ms^(-1),u_(2)=-10ms^(-1)`
Let the velocities after collision be `v_(1)andv_(2)`
`v_(1)=(m_(1)-m_(2))/(m_(1)+m_(2)).u_(1)+(2m_(2))/(m_(1)+m_(2)).u_(2)`
`=(10-20)/(10+20)xx20+(2xx20)/(10+20)xx(-10)`
`=(-20)/(3)-(40)/(3)=(-60)/(3)=-20ms^(-1)`
`v_(2)=(2m_(1))/(m_(1)+m_(2)).u_(1)+(m_(2)-m_(1))/(m_(2)+m_(2)).u_(2)`
`=(20xx10)/(10+20)xx20+(20-10)/(10+20)(-10)`
`=(40)/(3)-(10)/(3)=(30)/(3)=10ms^(-1)`