Answer to Question #90883 in Physics for Emma

Question

A jet plane is flying at mach 1.8 at an altitude of 10 km. If the sonic boom took 4.2 seconds to reach you and the average air temperature is 20c, how far has the plane traveled since it flew directly over your head?

Answer 1

The speed of sound is

$$c=343\frac{m}{s}$$

Mach angle:

$$\sin{\theta}=\frac{c}{v}=\frac{c}{1.8c}=\frac{1}{1.8}$$

The distance the plane traveled since it flew directly over your head:

$$d=h \cot{\theta}$$

$$d=10 \cdot{(\arcsin{\frac{1}{1.8}})}=15\ km$$