1.

A `10kg` ball and a `20kg` ball approach each other with velocities `20m//s` and `10m//s` respectively. What are their velocities after collision, if the collision is perfectly elastic ?

Answer» Here, `m_(1)=10kg, m_(2)=20kg`
`u_(1)=20m//s,u_(2)=-10m//s, upsilon_(1)=?, upsilon_(2)=?`
As the collision is perfectly elastic ,
`upsilon_(1)=((m_(1)-m_(2))u_(1))/(m_(1)+m_(2))+(2m_(2)u_(2))/(m_(1)+m_(2))`
`=((10-20)20)/(10+20)+(2xx20(-10))/(10+20)`
`upsilon_(1)=(-200)/(30)-(400)/(30)=(-600)/(30)=-20m//s`
and `upsilon_(2)=(2m_(1)u_(1))/(m_(1)+m_(2))+((m_(2)-m_(1))u_(2))/(m_(1)+m_(2))`
`=(2xx10xx20)/(10+20)+((20-10)(-10))/(20+10)=(300)/(30)=10m//s`


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