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.
`v_(1) = ((1-e)/(2))u` and `v_(2) = ((1+e)/2)u`

By law of conservation of momentum `mu + m xx 0 = mv_(1) + mv_(2)`
`rArr v_(1) + v_(2) = u` ..................(ii)
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 Eqs. (i) and (ii)
`2v_(2) = u + eu rArr v_(2) = [(1 +e)/(2)]u`
Subtracting Eq. (ii) from Eq. (i)
`2v_(1) = (1-e)u rArr v_(1)= [(1-e)/(2)]u`