In 1945, the united states tested the world’s first atomic bomb in what was called the trinity test. following the test, images were published showing the evolution of the blast. a few years later, a british scientist, by the name of g. i. taylor, used dimensional analysis to predict the amount of energy released by the trinity explosion, which was still classified information at the time. he did so, just by analyzing the images alone. he assumed the blast radius, r, depended only on the evolution time, t, the energy released, e, and the density of air, rho. using the buckingham-pi theorem, find the dimensionless group, π1 = k, where k is a constant. assuming k = 1, find the energy released, in tons of tnt, if the radius of the blast wave at t = 0.025s is r = 140m. take the density of air to be rho = 1.2kg/m3 . note, there are 4.184 × 109j per ton of tnt equivalent.