I am afraid that there is no exact answer to this. It all
depends on what happens to the bullets when they collide.
The two important laws that
govern such (in fact any) collision are:
Conservation of energy – the energy before impact
must be the same as the energy after impact.
Conservation of momentum – the
momentum after impact must be the same as the momentum before impact. In this case
since you have two bullets of the same mass moving at the same speed but in opposite
directions the total momentum of the system is zero. Momentum is a vector quantity and
since the directions of motion are opposite one of the bullets has negative momentum
compared with other.
Here is a set of possibilities.
1. A completely elastic
collision
All the kinetic energy is retained. The total must remain zero and so they simply
bounce off each other and return back along their original paths at the same
speed!
2. A completely inelastic collision.
All the kinetic energy is destroyed and
is converted into sound, heat, light and the deformation of the bullets as they collide and stick
together. In this case the bullets have no speed after collision and simply come to
rest.
3. Something in between.
Some of the kinetic energy is lost. There is some
deformation and sound etc. and the bullets bounce back along their original paths with
reduced speed.
4. The bullets break up on impact.
Some kinetic energy will be
lost. The total momentum of the fragments must be zero after collision. In other words some
move one way and some move the other. There is no way of knowing exactly how they may
break up and so we cannot really predict the speed of any
fragment.
