How do you find the kinetic energy of a gun?

Question

How do you find the kinetic energy of a 27 kg gun that has just fired a 52.2g bullet with a velocity of 317 m/s.

If the momentum of the bullet is 16.547 kg*m/s shouldt the momentum of the gun be the same?

Answer 1

Conservation of momentum

MgVg=MbVb

Vg=(Mb/Mg)Vb

Ke=0.5 Mg Vg ^2
Ke= 0.5 Mg [(Mb/Mg)Vb] ^2
Ke=0.5 [Mb Vb] ^2/Mg
Ke= 0.5 [ 0.0522 x 317]^2/ 27
Ke=5.1 Joules