If an airplane travels at a speed of 1120 km/hr at an altitude of 15 km, what is the required speed at an altitude of 8 km to satisfy Mach number similarity

1170 km/hr

Explanation:

Let's first state the formula to be used

c = √(KRT)

The temperature at an altitude of 15km is -56.5° C

Let's not convert this to °K, we have

-56.5° + 273.15 = 216.65° K

Also, the temperature at 8km is -36.9° C, on converting to °K we have

-36.9° + 273.15 = 236.25° K

Then again, we look for the speed at both 15 km and 8 km both of which are 295 m/s and 308 km

Finally, we use the mach similarity formula

(V/c) of 15km = (V/c) of 8km

V of 8km = c of 8km * (V/c) of 15km

V of 8km = 1170 km/hr