In July 16", 1945, the first explosion of an atomic bomb (Trinity test) occurred in the desert in New Mexico, unleashing the tremendous forces of nuclear energy to humanity and forever changing the world. The energy released by this first fission bomb was classified information. In 1950, images of the explosion were released and were published by Life magazine. The images included a time stamp and a scale bar. Using dimensional analysis (Buckingham Pi theorem), the British physicist G.I. Taylor estimated the energy released by the atomic bomb (he was remarkably accurate). This information, still classified, was thus made publicly available, which infuriated key people in the U.S. government. Here, you will follow Taylor's footsteps. This problem has historical significance. The atomic bomb released a shock wave, which is approximately spherical at early times. Assume that the energy released, E, depends upon the radius of the shock wave, R, the density of air, p, and time, t. (1) (ii) (iii) (iv) Write down these four variables, their units, and the dimensions involved. Using the Buckingham Pi theorem, form a dimensionless group that governs this system. Set the dimensionless group equal to a constant, c. Assume that this constant is approximately 1. Att 0.006s, the radius of the shock wave was 80 m. The density of air is 1.2 kg/m'. Estimate the energy released by the Trinity bomb.