An aeroplane is to move at Mesh number of 1.5 at altitude of 1000m. The atmosphere pressure and densities at this elevation are 89.89 KPa (abs) and $1.112 kg/m^3$ respectively. Calculate the speed of the plane in Km/h at this attitude. Assume ratio of specific heats k = 1.4. -

Given data- Mach No-1.5 The atmospheric pressure-59.59 Kpa ,density $(ρ)-1.112Kg/m^3,k-1.4$

$\hspace{1cm}$ $Pressure=59.59\times10^3pa \\ \text{Speed of sound,} c=\sqrt{\dfrac{k×p}{ρ}} =\sqrt{\dfrac{1.4×59.59×10^3}{1.112}}\\ ∴ \text{speed of sound at} 1000m =273.90m/s$

Now, Mach Number is,

$$M=\dfrac{\text{velocity of aeroplane}}{\text{velocity of sound in that medium}}\\ ∴ 1.5=\dfrac{\text{velocity of aeroplane}}{273.90}$$

Therefore, velocity of plane is$=273.90×1.5 \\ =410.85\\ \boxed{Answer =1479.06Km/h}$