Question

You are on the ground and observing a jet traveling in air at a constant height of 4500 m with a speed of 650 m/s. How long after the spaceship has passed directly overhead will the shock wave reach you

Answer 1

`t=11.1s`

Step-by-step explanation:

Given data

Jet Speed v=650 m/s=1.89504 mach

height h=4500 m

Speed of the Sound V=343 m/s

To find

time t

Solution

As we know that

`Vs_(Velocity)=d_(distance) /t_(time) \\d=Vs*t`

where

`Vs=1.895*V`

Also from trigonometric properties we know that

`tan\alpha =(Perpendicular)/(Base)`

We have use height h as perpendicular and distance d is base

So

`tan\alpha =h/d\\tan\alpha=h*(1/Vs*t)\\t=(h)/(tan\alpha ) (1)/(Vs)\\`

First we need to angle α

Since

`Sin\alpha =V/Vs`

`Sin\alpha =(v)/(1.895v)\\\alpha =32^(o)`

Substitute given values and angle to find

`t=(h)/(tan\alpha ) (1)/(Vs)\\t=(4500m)/(tan(32) ) (1)/(1.895*343m/s)\\t=11.1s`