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.
a) Find an expression for the bullet's speed in terms of k, d, M, m, and g.
b) What was the speed of a 13 g bullet if the block's mass is 2.5 kg and if the spring, with k = 50 N/m, was compressed by 48 cm?