An F-15 is in straight and level flight at about \(36,000 \mathrm{ft}\) where \(p_{\infty}=22,700 \mathrm{~N} / \mathrm{m}^{2}\). Its wing loading \(\left(W_{S}\right)\) is about \(400 \mathrm{~kg} / \mathrm{m}^{2}\). Assume \(\gamma=1.4\) and recall that wing loading is defined as the vehicle weight divided by the total wing area.

a. Use thin airfoil theory to develop an expression for the flight Mach number in terms of \(\propto, p_{\infty}, \gamma\) and the wing loading \(\left(W_{S}\right)\). Calculate the flight Mach number if \(\alpha=1.3^{\circ}\).

b. The aircraft's weight decreases over the course of the mission. How should the pilot change the angle of attack in order to maintain the same flight Mach number?