An explosion at ground level leaves a crater with a diameter that is proportiona

Question

An explosion at ground level leaves a crater with a diameter that is proportional to the energy of the explosion raised to 1/3 power; an explosion of 1 megaton of TNT leaves a crater with a 1 km diameter. Below Lake Huron in Michigan there appears to be an ancient impact crater with a 50 km diameter. What was the kinetic energy associated with that impact, in terms of
(a) megatons of TNT (1 megaton yields 4.2 x 10^15 J) and
(b) Hiroshima bomb equivalents (13 kilotons of TNT each)?

Please show the complete solution. Provide explanations as well. I'm not sure if I got the correct answers (they seem to have a very large value). Thanks. :)

Explanation / Answer

D=k(E)^(1/3) (and I will keep D in km and E in MT of TNT) Where k is a constant of proportionality. We also have 1=k*(1)^(1/3), k=1 (a) For D=50, E=(D^3), so E= 125000 MT or 125 GT (b) For hiroshima equivalents, that's 125000 MT / 13 KT = 125000 MT / 0.013 MT = 9615384.6 hiroshima bombs.

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