What is the altitude of the plane?

[jrzygrl]

Homework Statement

A jet fighter in level flight passes directly overhead at a speed corresponding to Mach number 1.29. The sonic boom is heard by you on the ground 11.9 s later. What is the altitude of the plane? Assume (unrealistically) the speed of sound does not change with altitude.

Homework Equations

Mach = vsource / vsound

The Attempt at a Solution

M = vsource / vsound
1.29 = vsource / 343
vsource = 442.47 m/s

d = vt
d = (442.47 m/s)(11.9 s)
d = 5265.393m = 5.265 km

the answer above was wrong, any help is appreciated!

 

[KalvinDeathX]

Ok, well, to start, are you sure that 343m/s is the correct number? Because it varies depending on temperature, humidity and many other factors. It would probably be helpful if it was one of the givens.

 

[KalvinDeathX]

And why would you put the speed of the jet into D=VT? You put T as the time it took the SOUND to reach you from the point it was exerted(which we will call point A), so you should probably put V as the speed of sound. This will tell you how far away Point A is, which will tell you how high up the plane was.

 

[tiny-tim]

… one step at a time …

d = vt
d = (442.47 m/s)(11.9 s)
d = 5265.393m = 5.265 km

Hi jrzygrl!

No no no …

All you've calculated is the horizontal distance traveled by sound in 11.9s.

How does that give you its height?

Think … do it one step at a time … can you hear the plane as it approaches? can you hear it when it's overhead (position O, say)? Where is it when you can first hear it (position F, say)? How long does the plane take to get from O to F? How long does the sound take to get from F to J (that's you)?

Then draw the triangle OFJ …

 

[Dick]

Draw a right triangle with you at one vertex, the plane at 11.9sec later at another and the place where the plane was when it was directly overhead at the right angle. If you just heard the boom then the hypotenuse is the shock wave. The horizontal leg is the velocity of the plane times 11.9sec, right? You want to solve for the vertical leg. To solve it by trig you need to know one more thing about the triangle. Can you use the given information to find the angle between the shock wave and the horizontal?

 

[KalvinDeathX]

Why would you do that? D=VT works just fine for this situation.

 

[tiny-tim]

… one step at a time …

The horizontal leg is the velocity of the plane time 11.9sec, right?

Wrong! Do it step by step …

 

[Dick]

Wrong! Do it step by step …

It is so. :) I defined the triangle that way.

 

[Dick]

Why would you do that? D=VT works just fine for this situation.

If you are saying that the distance from you to the plane when you hear the boom is V_sound*11.9sec, you are quite wrong. The plane is traveling FASTER than sound. It's a shock wave.

 

[KalvinDeathX]

No, I'm saying the distance from you to the point directly above you at the height where the plane passed. I'm not saying I'm right though.
If a sonicboom works this way, then I am probably wrong -> upload.wikimedia.org/wikipedia/commons/b/b3/Sonic_boom.svg
I just assumed the sound might travel straight down, but now I think that it comes out in a cone, which would make trig necessary.

 

[Dick]

No, I'm saying the distance from you to the point directly above you at the height where the plane passed.

Also untrue. You hear the sound when the shock front passes. The point on the shock front that hits you actually originated from the plane before it passed overhead. There's a picture at http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/sound/u11l3b.html .

 

[jrzygrl]

thanks a lot guys i found the answer!