MASA, the Michigan Aeronautical Science Association, exists to design, fabricate, and test an increasingly-impressive series of rockets. Two tests of their 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 (SI units of kg/m3), the local gravitational acceleration g (SI units of m/s2), the atmospheric kinematic viscosity (SI units of m2/s), and the atmospheric sound speed a (SI units of m/s). (a) [4 pts] How many dimensionless groups are necessary to describe this problem, and why? (b) [8 pts] Using {E, g, } as your K-set, use a standard Buckingham- dimensionless anal- ysis to find the exponents for a safe-radius coefficient of the form R = REg Show your work for full credit! 2