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 and stops in the block. The spring’s maximum compression d is measured.
a. Find an expression for the bullet’s speed v_B in terms of m, M, k, and d.
b. What was the speed of a 10 g bullet if the block’s mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 45 cm?