Answer:
[tex]t=11.1s[/tex]
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
[tex]Vs_{Velocity}=d_{distance} /t_{time} \\d=Vs*t[/tex]
where
[tex]Vs=1.895*V[/tex]
Also from trigonometric properties we know that
[tex]tan\alpha =\frac{Perpendicular}{Base}[/tex]
We have use height h as perpendicular and distance d is base
So
[tex]tan\alpha =h/d\\tan\alpha=h*(1/Vs*t)\\t=\frac{h}{tan\alpha } \frac{1}{Vs}\\[/tex]
First we need to angle α
Since
[tex]Sin\alpha =V/Vs[/tex]
[tex]Sin\alpha =\frac{v}{1.895v}\\\alpha =32^{o}[/tex]
Substitute given values and angle to find
[tex]t=\frac{h}{tan\alpha } \frac{1}{Vs}\\t=\frac{4500m}{tan(32) } \frac{1}{1.895*343m/s}\\t=11.1s[/tex]
