It has been said that sometimes lead bullets melt upon impact. Assume that a bullet with an initial temperature of 301 K receives 73.9 % of the work done on it by a wall on impact as an increase in internal energy. (The melting point of lead is 601 K, the heat of fusion for lead is L = 23.2 kJ/kg, and the specific heat of lead is c = 0.129 kJ/kg K.)

a) What is the minimum speed with which a 14.1-g lead bullet would have to hit a surface (assuming the bullet stops completely and all the kinetic energy is absorbed by it) in order to begin melting?
b) What is the minimum impact speed required for the bullet to melt completely?