Question

A bullet of mass a and velocity b is fired into a large block of mass c.Then how the final velocity of the system is ab/a+c?

Answer 1

Initial momentum of the system=a*b
Final momentum of system=(mass of bullet+mass of large block)*final velocity
=(a+c)*x   (x=final velocity)
According to law of conservation of momentum
initial momentum=final momentum
a*b=(a+c)*x
ab/(a+c)=x

Answer 2

Because we would consider that the bullet is still stuck inside the block, hence the masses would be added.

1) Initial momentum of the system would be p = mass * velocity = ab

2) Final momentum of the system would be p` = new mass * velocity.

3) Assuming, complete transfer of energy,

new mass = a + c ( mass of block + mass of bullet )

since, the bullet is stuck inside the block.

4) New momentum would be

p` = (a+c) * v`

5) By conservation of momentum :

ab = (a+c) * v`

v` = ab/ (a+c)