Time of your life

You're watering the plants in your garden when you notice an atomic bomb has been set off 400 m from your garden. At time t=4.3t = 4.3 ms after the explosion, the fireball is 330 m away.

How much time do you have before you're vaporized by the advancing fireball?

Assumptions

  • An insignificant amount of energy is lost to dissipative processes.
  • The fireball's advancing front is roughly spherical.
  • The surrounding atmosphere has a density of ρ\rho kg/m3\mbox{kg/m}^3.
  • The ambient pressure, in the face of the bomb energy, is completely irrelevant.
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