# Getting different velocity from momentum conservation and work energy theorem

Consider a system of bullet (of mass 5 kg) and block (of mass 20 kg). Initially the block is at rest and the bullet moves towards it at 30 m/s. After penetrating the block, the bullet comes out with speed 10 m/s. What is the velocity of block?

My attempt
As there is no external force in the system, momentum of the system of particles remain conserved.
Initial momentum= Final momentum
$$5\times 30 = 20\times v+ 5\times 10$$
$$\implies v = 5 m/s$$

Another approach
When block penetrates the block it experiences a retarding force $$f$$ from the block and the block experiences the same force which accelerates it.
For bullet, $$10=30-\frac{F}{5}t$$.
$$\implies Ft=100$$

For block, $$v=\frac{F}{20}t$$
$$\implies v=5 m/s$$

Using work energy theorem
Work done against on the bullet by the force f = Initial KE of bullet - Final KE of bullet
= $$\frac{5}{2}(30^2-10^2)=2000J$$
This energy basically goes as KE of the block.
2000=Final KE of block - Initial KE of block
$$\implies \frac{20}{2}v^2=2000$$.
$$\implies v^2=200$$
$$\implies v=10\sqrt 2$$

The correct answer is 5 m/s.
Why am I getting incorrect answer with the Work energy theorem?