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 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 60 km diameter. What was the kinetic energy associated with that impact, in terms of (a) megatons of TNT (1 megaton yields 4.2 × 1015 J) and (b) Hiroshima bomb equivalents (13 kilotons of TNT each)? (Ancient meteorite or comet impacts may have significantly altered Earth's climate and contributed to the extinction of the dinosaurs and other life-forms.)

Explanation / Answer

D = k(E)^(1/3)

Where

D is 1 km and E is 1 MT of TNT

k is a constant of proportionality.

We also have

1 = k*(1)^(1/3),

k = 1

(a) For D = 60 km,

D = k(E)^(1/3)

D = 1*(E)^(1/3)

E = (D^3),

so E= 60^3

       = 216000 MT or 216 GT

(b) For hiroshima equivalents, that's 216000 MT / 13 KT

                                                 = 216000 MT / 0.013 MT

                                                 = 16,615,385 hiroshima bombs.

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