Different result with kinetic energy and momentum when a bullet hits a target

[BWR]

TL;DR

kinetic energy and momentum give different result.

A bullet hits a target. Assume that all the energy is transferred to the target without destroying it.
I want to know the target’s velocity after the impact.

bullet: m₁= 123 kg, V_x= 2, V_y= 3, V_z= 4.
target: m₂= 999 kg

Calculations using kinetic energy
Ec_bullet = .5 * m₁ * V² = 1783.5 J
V_target² = Ec_bullet * 2 / m₂, V_target = 1.8896 m/s

Since I'm particularly interested in V target along the Z axis, I calculate:

Vz_target² = (.5 * m₁ * V_z²) * 2 / m₂, Vz_target = 1.40356 m/s


Calculations using momentum
p_bullet = m₁ * V = 662.375 kgm/s
V_target = p_bullet / m₂ = 0.663038 m/s which is different from 1.8896 m/s.

Where I'm wrong?

 

[Ibix]

Is the collision elastic or inelastic?

 

[haruspex]

Your first calculation doesn’t assume "all the energy is transferred to the target". It assumes the target gets all the energy the bullet originally had, but says nothing about the energy the bullet is left with. If you were to continue and calculate that you would find it still has rather a lot, so you have not assumed energy conservation.

The problem is that a collision with a stationary object can only transfer all of the energy if the bodies have equal mass. Instead, try specifying a coefficient of restitution parameter and finding the value which maximises the energy acquired by the target.

Also, as a matter of technique, never plug in numerical values until you have to. Keep the working entirely symbolic. It has many, many advantages.