A 0.940 kg block is attached to a horizontal spring with spring constant 2550 N/m. The block is at rest on a frictionless surface. A 7.90 g bullet is fired into the block, in the face opposite the spring, and sticks.

Question

What was the bullet's speed if the subsequent oscillations have an amplitude of 10.2 cm?

Answer 1

The spring's potential energy at maximum compression (when X is the amplitude of viration) equals the initial kinetic energy at zero deflection, after the bullet hits.

Use that fact to get the initial velocity of the vibrating Bullet-Block combo.

Then use conservation of momentum to get the velocity of the bullet before impact.