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 the separates from the spring.

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?