An airplane is flying at Mach 1.48 at an altitude of 7,800.00 meters, where the speed of sound is v = 311.83 m/s. How far away from a stationary observer will the plane be when the observer hears the sonic boom? (Enter the total distance in m.)

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