Two identical blocks `A` and `B` connected by massless string, are placed on a frictionless horizontal plane. A bullet havig the same mass, moving with speed `u` strickes block `B` from behind as shown. If the bullet gets embedded into block `B` then find

a. the velocity of `A,B,C` after collision.
b. impulse on `A` due to tension in the string,
c. impulse on `C` due to normal force of collision,
d. impulse on `B` due to normal force of collision.

Explanation

Let us assume that all the three are move with velocity v

Take rightward direction is +ve. Then first we write impulse equation on bullet
`-intNdt=mv-mu` …(1)
Now impulse equation on block B
`int(N-T)dt=mv` ….(2)
Impulse equation on block A
`intT.dt=mv` ....(3)
Impulse on B due to normal force of collision from eq. (2)
`int(N-T)dt=(mu)/3`
`intN.dt=(mu)/3+intT.dt=(mu)/3+(mu)/3=(2mu)/3`