1. (30 points). Consider an aircraft climbing steadily in the Earth's atmo- sphere with a constant speed of 1100 km/hr. As the aircraft goes to higher altitudes, the temperature of the

air changes approximately linearly with elevation at a rate of -6.6 °C/km. Assume that the temperature at sea level is 25 °C. (a) Compute the Mach number of the aircraft when it reaches an altitude of 3000 m. (b) Compute the Mach number of the aircraft when it reaches an altitude of 15000 m. (c) How does the Mach number of the aircraft vary with elevation? At what altitude does the flow around it become sonic?