Designing a Ballistic Spring System for Measuring Bullet Speed

[killersanta]

Homework Statement

You have been ask to design a "ballistic spring system" to measure the speed of bullets. A bullet has a mass of m is fired into a block with mass M. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k. The opposite end of the spring is anchored to a wall. The spring's maximum compression is d is measured.

A. Find a expression for the bullet's speed VB in terms of m, M, k, d.
B. Not help is needed
C. " "

Homework Equations

I think,
Pi = Pf
Ki + Ui = Kf + Uf

The Attempt at a Solution

mVB + MV0 = (m + M)V1

MV0 goes to 0

Equation 1. VB = (m + M)V1
......m
________________________
.5(m + M)V1^2 + (m + M)gy1 = .5(m + M)V2^2 + (m + M)gy2 + .5kd^2

Having the Y axis start at the bullets height - (m + M)gy1, (m + M)gy2 go to 0

.5(m + M)V2^2 I think goes to 0

Equation 2. V1 = Sq. Rt.(kd^2/(m + M))

Plug 1 into 2

VB = Sq. Rt. ((m + M)^2kd^2/ m^3 + Mm^2)


I don't know. I tried so many things... just not getting it...

 

[killersanta]

Wow, just realize if i would have factor better:
VB = Sq. Rt. ((m + M)^2kd^2/ m^3 + Mm^2)

Becomes VB = Sq. Rt.((m + M)kd^2/m^2)

Which is the answer the book had.