Answer:
The plane will be 11545.46 m far when the observer hears the sonic boom
Explanation:
Step 1: Data given
Altitude of the plane = 7800 meters
speed of sound = 311.83 m/s
Step 2:
The mach number M = vs/v
This means v/vs = 1/M
Half- angle = ∅
sin∅= v/vs
∅ = sin^-1 (v/vs)
∅ = sin^-1 (1/M)
∅ = sin^-1(1/1.48)
∅= 42.5 °
tan ∅ = h/x
⇒ with h= the altitude of the plane = 7800 meter
⇒ with x = the horizontal distance moved by the plane
x = h/tan ∅
x = 7800 / tan 42.5
x = 8512.2 meters
d = the distance between the observer and the plane when the observer hears the sonic boom is:
d = √(8512.2² + 7800²)
d = 11545.46 m
The plane will be 11545.46 m far when the observer hears the sonic boom
