What Is the Altitude of a Plane Traveling at Mach 2.5?

[jvdamdshdt]

Homework Statement

A plane is traveling at Mach 2.5. An observer on the ground hears the sonic boom 1.0min after the plane passes directly overhead.

What is the plane's altitude? Ignore the change in the speed of sound with the altitude.

Homework Equations

v=d/t
1/T= f

The Attempt at a Solution

Hey guys I am having trouble with this problem.
I tried changing mach to velocity = 857.5 m/s and I tried 850 m/s
Time 60 seconds

I've tried v x t = d
My answers are 51000 m and 51450 m
I have no idea where I am going wrong.

I also tried to find the wavelength and using that as an answer but it was wrong also.

 

[SteamKing]

The OP only has half a question. Are you supposed to estimate the observer's distance to the plane? The altitude? What??

 

[NascentOxygen]

A plane is traveling at Mach 2.5. An observer on the ground hears the sonic boom 1.0min after the plane passes directly overhead.

Hi vdamdshdt, is there a question associated with this scenario?

 

[jvdamdshdt]

Hi vdamdshdt, is there a question associated with this scenario?

Yes. I fixed it.

 

[SteamKing]

Homework Statement

A plane is traveling at Mach 2.5. An observer on the ground hears the sonic boom 1.0min after the plane passes directly overhead.

What is the plane's altitude? Ignore the change in the speed of sound with the altitude.

Homework Equations

v=d/t
1/T= f

The Attempt at a Solution

Hey guys I am having trouble with this problem.
I tried changing mach to velocity = 857.5 m/s and I tried 850 m/s
Time 60 seconds

I've tried v x t = d
My answers are 51000 m and 51450 m
I have no idea where I am going wrong.

I also tried to find the wavelength and using that as an answer but it was wrong also.

Do you understand the concept of the Mach cone and the Mach angle? An observer on the ground cannot hear a supersonic plane until the shock wave has passed him.

 

[jvdamdshdt]

Do you understand the concept of the Mach cone and the Mach angle? An observer on the ground cannot hear a supersonic plane until the shock wave has passed him.

I don't completely understand the shock wave and supersonic plane. My professor lectures and gives us a quiz then a homework to do on MasteringPhysics. He did not go over this portion but I've read the textbook. From my reading I think that the speed of the shock wave is it's own separate thing from the speed of the plane. The guy on the ground hears a shock wave after 1 min. Which means he heard the sound moving at 344 m/s after 60 secs. Someone please tell me if I am going in the right direction.

 

[jvdamdshdt]

So I've figure it out. Thanks SteamKing. Using sin θ = Vsound/Vobj . I found angle the the object. I've then continued with Tan θ = opp/adj . Adj = distance traveled in 60 sec. Mach 2.5 x 334 x 60 sec = 50400 m . Plug the angle and distance traveled into the formula Tan θ = opp/adj . I hope this helps the next person taking a physics class.