An object of mass m moving with speed u collides one dimentionally with another identical object at rest. Find their velocities after collision, if coefficient of restitution of collision is e.

Explanation

Let `v_(1) and v_(2)` be the final velocities of 1st and 2nd object respectively

By law of conservation of momentum `m u+mxx0=mv_(1)+mv_(2)`
`rArr" "v_(1)+v_(2)=u" …(i)"`
Now,
`e=(v_(2)-v_(1))/(u_(1)-u_(2))`
`rArr" "(v_(2)-v_(1))/(u)=e`
`rArr" "v_(2)-v_(1)=eu" ...(ii)"`
Adding (i) and(ii)
`2v_(2)=u+eu`
`rArr" "v_(2)=[(1+e)/(2)]u`
Subtracting (ii) from (i)
`2v_(1)=(1-e)u`
`rArr" "v_(1)=[(1-e)/(2)]u`