Air enters the combustor of a scramjet engine at $M=2.5$ and $T_{0}=1500 \mathrm{~K}$ and $P_{0}=1 \mathrm{MPa}$. Kerosene with calorific value of $45 \mathrm{MJ} / \mathrm{kg}$ is used as the fuel. Determine the fuel-air ratio (on a mass basis) that will result in the exit Mach number being equal to 1. Also determine the fuel-air ratio that will result in an "inlet interaction" i.e., a normal shock stands just at the entrance of the combustor.