need help please with physics?

Question

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass 2.90 g is fired into a block of mass 1.80 kg. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k=32.0 N/m. The opposite end of the spring is anchored to a wall. What was the speed of the bullet if the spring's maximum compression is 14.4 cm?

Answer 1

The spring compresses .144 m with a constant of 32 N/m so the amount of energy in it is
32*(.144)²/2 = .332 J Since this is the kinetic energy of the bullet (given by mv²/2) the original velocity is
v = √(2*.332/.0029) = 15.13 m/s

HTH ☺


Doug