A ball of mass `4 kg` moving with a velocity of `12 m//s` impinges directly on another ball of mass `8 kg` moving with velocity of `4 m//s` in the same direction. Find their velocities after impact and calculate the loss of `KE` due to impact if `e =0.5`.

Explanation

`u_(1)=12m//s" "m_(1)=4kg`
`u_(2)=4m//s" "m_(2)8kg`
Let `v_(1)` and `v_(2)` be the velocity after impact.
By conservation of momentum:
`m_(1)v_(1)+m_(2)v_(2)=m_(1)u_(1)+m_(1)u_(2)`
`rArr" "4v_(1)+8v_(2)=80` ...(i)
By Newton's experimental Law:
`v_(2)-v_(1)=e(u_(1)-u_(2))`
`v_(2)-v_(1)=0.5(12-4)=4`...(ii)
Solving (i) and (ii), we get:
`v_(1)=4m//s` and `v_(2)=8m//s`