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I'm having a bit of a problem with the following problem:

A supersonic airplane flying at the velocity v is flying horizontally to the ground with altitude h. At the exact moment when the plane is vertically above a listener on the ground, it emits a sound. It takes Δt seconds for the sound to reach the listener. What is the velocity of the airplane if the speed of sound is c.

The solution given is v=c/√(1-(c*Δt/h)^2). It's short so I'm not using latex :)

Anyway, my reasoning is that the sound will go straight down with speed c, since it can't go any faster. But then, this height h=c*Δt, and if you try putting that in the answer bad things happen.

Could someone explain why h =/= c*Δt and how to get that weird proportion. At least give me some hints :)

Thank you very much!