Instead of a Ballistic Pendulum We Could Use a System $\times$

Multiple Choice

Instead of a ballistic pendulum we could use a system where the bullet (mass = m) is fired into a block (mass = M) that is coupled to an uncompressed spring (with spring constant k) .The speed of the bullet,v,can be found by measuring the maximum distance,d,of compression of the spring.In this situation the initial speed of the bullet is given by:

A) (k $\times$ (M+m) ) ^1/2 $\times$ d/M
B) (k $\times$ (M) ) ^1/2 $\times$ d/m
C) (k $\times$ (M+m) ) ^1/2 $\times$ d/m
D) (k $\times$ (M-m) ) ^1/2 $\times$ d/m
E) (k $\times$ (M+m) ) ^1/2 $\times$ d/2m