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## 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.

## Homework Equations

KEi + PEi = KEf +PEf

F= -kx

## The Attempt at a Solution

I first used Newtons second law to find the the distance x the string is stretched, so:

Mg=k(x-d)

x= (Mg/k)+d

Then I used the energy law like so:

1/2(m

_{b}(V

_{b})

^{2}+Mgy + 1/2(k)(x

^{2}) = Mg(y+d)

solving for V

_{b}I get:

sqrt[(2Mgd-(k(d+Mg/k)^2))/m]

But I am pretty sure this is wrong, can someone help me