How do you calculate the speed of a bullet using a ballistic spring system?

[1831]

Homework Statement

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block. The spring's maximum compression d is measured.

Find an expression for the bullet's speed.
Express your answer in terms of the variables m, M, k, d, and constant g.

Homework Equations

Ki + Ug + Usp = Kf + Ug + Usp

The Attempt at a Solution

I used conservation of momentum to find the final velocity of the bullet+block

(m+M)vf=mvi + Mvi

so...

vf=(m/m+M)*vB

where vB is the initial speed of the bullet.

Next, I used:
Ki + Ug + Usp = Kf + Ug + Usp

(1/2)mvi^2 + (1/2)kd^2 + Mgd = (1/2)mvf^2 + (1/2)kd^2 + Mgd
0 + (1/2)kd^2 + 0 = (1/2)(m+M)[(m+M)^2*vB^2] + 0 + Mgd

I found the answer to be:

((kd^2 - Mgd)(m+M))/m^2 = Vb

but this was not correct...please help me.

 

[1831]

I got it...nevermind

 

[dif1520]

Could someone please explain this, I got the following, but it is not correct

vB = (k*d^2(m + M))/m^2

I figured it out, i was missing the square root. The answer is:

vB = sqrt((k*d^2(m + M))/m^2)