A turbojet powered aircraft is flying at Mach number 0.8 at an altitude of10 km. What is the thrust of the engine?

Mach number is given as (velocity of the aircraft / speed of the sound).

$$M=\frac{V}{a}$$

Speed of sound is given as $$U_{\infty }={M}{a} \\=0.8\times 299.5 \\=239.6\;m/s$$

Mass flow rate of air through the inlet is $$\dot{m}_{a}=\rho _{\infty }u_{\infty}A_{i} \\=0.413\times 239.6\times 0.7 \\=69.27\;kg/s$$

Thrust of the engine is given as

$$T=\dot{m}_{a}\left [ \left ( u_{e}-u_{\infty } \right )+\left ( P_{e}-P_{\infty } \right ) \right ]A_{e}$$
$$\Rightarrow T=69.27 \left [ \left ( 500-239.6 \right )+\left ( 60-26.5 \right ) \right ]\times 10^{3}\times 0.4$$

$$=31.44\;kN$$