1. (30 points). Consider an aircraft climbing steadily in the Earth's atmo- sphere with a constant s ...

Expert Answer

We are given the following information:

• The speed of the aircraft v=1100 km/hv = 1100 \, \text{km/h}v=1100km/h (which we will need to convert into m/s).
• The rate of temperature change with altitude is given by −6.6 °C/km-6.6 \, \text{°C/km}−6.6°C/km.
• The temperature at sea level is T0=25 °CT_0 = 25 \, \text{°C}T0?=25°C.
• The speed of sound ccc in air varies with temperature according to the formula: c=γRTc = \sqrt{\gamma R T}c=γRT? where:
  • γ=1.4\gamma = 1.4γ=1.4 (ratio of specific heats for air),
  • R=287 J/kg\cdotpKR = 287 \, \text{J/kg·K}R=287J/kg\cdotpK (specific gas constant for air),
  • TTT is the temperature in Kelvin.

Let's first convert the speed of the aircraft into m/s:

v=1100 km/h=1100×10003600=305.56 m/sv = 1100 \, \text{km/h} = \frac{1100 \times 1000}{3600} = 305.56 \, \text{m/s}v=1100km/h=36001100×1000?=305.56m/s