Question

Assume you visit a world where the atmosphere is made of hydrogen (the planet is massive and holds onto this gas). Your spacecraft can fly at Mach 20 on Earth, as measured by sound at 5°C. On this planet, what is your Mach number if the speed of sound in hydrogen is 1,267 m/s?

Answer 1

Given,

The Mach number of the aircraft on the earth, M₁=20

The temperature at which the Mach number was measured, T=5 °C

The speed of sound in hydrogen, v=1267 m/s

The speed of the sound at 5 °C is u=334.4 m/s

The Mach number of the aircraft on the earth is given by,

`M_1=(v_0)/(u)`

Where v₀ is the speed of the aircraft.

On substituting the known values,

`\begin{gathered} 20_{}=(v_0)/(334.4) \\ v_0=20*334.4 \\ =6688\text{ m/s} \end{gathered}`

The Mach number of the other world is given by,

`M_2=(v_0)/(v)`

On substituting the known values,

`\begin{gathered} M_2=(6688)/(1267) \\ =5.28 \end{gathered}`

Thus the Mach number on the other world is 5.28