Watching a jet plane fly high over my head, I noticed that the sound seemed to be coming from directly above me when the plane was at an angle of 30 degrees from vertical. How fast was the plane flying? Assume the speed of sound was 330 m/s.

Answer 1

Let the plane be H m above the observer.
Time taken for sound to reach observer, t
= H/330 s
Distance plane travelled in time t, D
=H sin(30°) m
Speed of plane
= distance / t
= D/t
= H sin(30°) / (H/330) m/s
= 330 sin(30°) m/s
Convert to km/h if necessary (multiply by 3.6).