Question

A jet plane passes over you at a height of 5870 m and a speed of Mach 1.47. (a) Find the Mach cone angle. (b) How long after the jet passes directly overhead does the shock wave reach you

Answer 1

Answer:

(a) Angle is 42.865°

(b) t=12.54s

Explanation:

The jet plane is at 5870m from Earth surface

The jet traveling at speed of 1.47 Mach

Speed of Sound v=343 m/s

Part (a)

As we know :

$Sin\alpha =\frac{v}{vs}$

Substitute the given values

$Sin\alpha =\frac{v}{1.47v}\\ Sin\alpha =\frac{343m/s}{1.47(343m/s)} \\Sin\alpha =0.68027\\\alpha =Sin^{-1}(0.68027)\\\alpha =42.865^{o}$

Angle is 42.865°

Part (b)

As the distance given as:

$d=vst$

By using some trigonometry

$d=\frac{h}{tan\alpha }$

Where h is the height of jet plane

Thus

$t=\frac{h}{tan\alpha } \frac{1}{vs}$

Substitute the given values

So

$t=\frac{5870m}{tan(42.865)}\frac{1}{1.47(343m/s)} \\t=12.54s$