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

(a) Angle is 42.865°

(b) t=12.54s

Step-by-step 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 =(v)/(vs)\\`

Substitute the given values

`Sin\alpha =(v)/(1.47v)\\ Sin\alpha =(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=(h)/(tan\alpha )`

Where h is the height of jet plane

Thus

`t=(h)/(tan\alpha ) (1)/(vs)`

Substitute the given values

So

`t=(5870m)/(tan(42.865))(1)/(1.47(343m/s)) \\t=12.54s`