Two early hybrid rocket tests showed that a malfunctioning rocket is indistinguishable from a bomb. Shell fragments from a zero-altitude explosion travel a distance R that can be considered a function of the following parameters: the characteristic size L of the fragment (SI units of m), the available combustion energy E within the chamber (SI units of J), the rocket casing density p (SI units of kg/m3), the local gravitational acceleration g (SI units of m/s2), the atmospheric kinematic viscosity v (SI units of m2/s), and the atmospheric sound speed a (SI units of m/s). (a) How many dimensionless groups are necessary to describe this problem, and why? (b) Using {E,g,o} as your K-set, use a standard Buckingham-II dimensionless analysis to find the exponents for a safe-radius coefficient of the form. Show all steps II R = , V BY c) Using the same K-set, use a standard Buckingham-II dimensionless analysis to find the exponents for a viscosity-scaling coefficient of the form. Show all steps VE g pr = RE gp'