energy/momentum physics problem?

Question

Can anyone solve this for me please im stumped

A 5-g bullet is discharged at 350 m/s into a mass-spring system. If the mass is 10 kg and the spring constant is 150 N/m, how far will the spring be compressed if the bullet stays in the mass?

Answer 1

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Conservation of momentum during the collision

0.005(350) + 10(0) = 10.005v

v = 0.1749 m/s

The kinetic energy will convert to spring potential if we ignore friction 

½(10.005)(0.1749)² = ½(150)x²

x = 0.04517...m or about 45 mm

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