# Math Help - Filming a plane breaking the sound barrier?

1. ## Filming a plane breaking the sound barrier?

I'm watching a video of a plane breaking the sound barrier, trying to determine if it's a hoax. Can a cameraman pan fast enough to capture the plane?

Assuming the plane is traveling the speed of sound at sea level, 340.29m/s squared, how would I calculate the distance the cameraman is from the plane?

2. First, I don't believe that the plane in the video is going faster than the speed of sound, because you can hear it in the video before it passes by. If it was going faster than sound, then you wouldn't hear it until after it had gone by. You would also hear the sonic boom just as the plane passes, which is not evident in this video.

But regradless of how fast the plane was going I don't see why it would be impossible to pan the camera and follow it, as long as it is far enough away. Using your numbers - at 340 m/s (note - the correct units for velocity is meters per second, not meters per second squared) if the plane is 100 meters away at its closest approach then the "panning speed" as it passes by is:

$
\omega = \frac v r = \frac {340m/s} {100m} = 3.4 \ radians/sec = 194 \ degrees/sec
$

It's not impossible to pan that quickly, but the video does look slower than that.

If this was the "Myth Busters" TV show I'd say ... "Busted!"