A textbook of mass 2kg sits on a spring of spring constant 400 N/m. A bullet of mass 10g is fired below with a speed of 600 m/s and becomes lodged into book.
a) What distance is the book going to climb with respect to its initial position before momentarily coming to a stop?
b) After the book starts falling again, is it going to stop below or above its initial position?
Hint: First you need to check whether or not the separates from the spring.

ebaines

First, determine how far the spring is compressed with the weight of the book on it, from kx= mg. Then conservation of momentum to determine the initial velocity of the book/bullet combination after the bullet strikes: (M_bullet + M_book)*v = M_bullet* 600m/s. Then conservation of energy in the spring mass system to determine how much it occilates after the bullet hits it: 1/2 k x^2 = 1/2 (M_bullet + M_book) v^2 -- here x is measured from the initial deflection point of the spring/book system. That should answer part A. As for part b: it's pretty obvious - what do you think?