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.
KEi + PEi = KEf +PEf
The Attempt at a Solution
I first used Newtons second law to find the the distance x the string is stretched, so:
Then I used the energy law like so:
1/2(mb(Vb)2 +Mgy + 1/2(k)(x2) = Mg(y+d)
solving for Vb I get:
But I am pretty sure this is wrong, can someone help me