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

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Homework Help Overview

The problem involves a plane traveling at Mach 2.5 and an observer on the ground hearing the sonic boom 1.0 minute after the plane passes overhead. The objective is to determine the altitude of the plane while ignoring the change in the speed of sound with altitude.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss converting Mach speed to velocity and calculating distance using time. There are attempts to apply the formula v = d/t, but results vary significantly.
  • Some participants question whether additional information, such as the observer's distance from the plane, is needed to solve the problem.
  • There is a mention of the Mach cone and the Mach angle, with some participants expressing uncertainty about the relationship between the speed of the plane and the speed of the shock wave.
  • One participant reflects on their understanding of the shock wave and its propagation, indicating a need for clarification on these concepts.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some guidance has been offered regarding the Mach cone and the relationship between the plane's speed and the shock wave, but no consensus has been reached on the correct approach to find the altitude.

Contextual Notes

Participants note that the original poster's understanding of the problem may be incomplete, and there is a lack of clarity regarding the assumptions that can be made about the observer's position relative to the plane.

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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.
 
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The OP only has half a question. Are you supposed to estimate the observer's distance to the plane? The altitude? What??
 
jvdamdshdt said:
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? :wink:
 
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NascentOxygen said:
Hi vdamdshdt, is there a question associated with this scenario? :wink:

Yes. I fixed it.
 
jvdamdshdt said:

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.
 
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SteamKing said:
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.
 
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.
 

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