Question

An airplane is flying at Mach 1.58 at an altitude of 7,100.00 meters, where the speed of sound is v = 314.75 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.)

Answer 1

M = mach number = 1.58

$\theta$ = angle of the mach cone

we know that

Sin$\theta$ = 1/M

Sin$\theta$ = 1/1.58

$\theta$ = Sin^-1(1/1.58)

$\theta$ = 39.3 deg

d = distance from the stationary observer = ?

H = altitude = 7100 m

In the mach cone

tan$\theta$ = H/d

tan39.3 = 7100/d

d = 8674.5 m