Problem: An explosion at ground level leaves a crater with a diameter that is proportional to the energy of the explosion raised to the 1/3 power; an explosion of 1 megaton of TNT leaves a crater with a 1 km diameter. An ancient impact crater is found with a 52 km diameter.
Part A: What was the kinetic energy associated with that impact, in terms of:
(a) megatons of TNT (1 megaton yields 4.2 x 1015 J) and
(b) Hiroshima bomb equivalents (13 kilotons of TNT each)?
Please give a full detailed explanation of solution for above problem.