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Subject: "Bullet Sound"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #49
Reading Topic #49
Kenneth Arceo (Guest)
guest
Dec-11-00, 01:41 PM (EST)
 
"Bullet Sound"
 
   A bullet is fired horizontally at a target, and the sound of its impact is heard 1.5 seconds later. If the speed of the bullet is 3,300 meters per second and the speed of sound is 1,100 meters per second, how far away is the target?


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  Subject     Author     Message Date     ID  
Bullet Sound Kenneth Arceo (Guest) Dec-11-00 TOP
  RE: Bullet Sound th Aug-14-01 1
     RE: Bullet Sound stan Nov-15-04 7
     RE: Bullet Sound ry Nov-17-04 8
  RE: Bullet Sound Airborne Bob Oct-04-04 2
  RE: Bullet Sound ECON Oct-07-04 3
     RE: Bullet Sound rewboss Oct-08-04 4
         RE: Bullet Sound ECON Oct-12-04 5
             RE: Bullet Sound Airborne Bob Oct-13-04 6
  RE: Bullet Sound lokesh gupta Nov-20-04 9

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th
Charter Member
3 posts
Aug-14-01, 08:15 PM (EST)
Click to EMail th Click to send private message to th Click to add this user to your buddy list  
1. "RE: Bullet Sound"
In response to message #0
 
   The time it takes to get to the target that is x meters away is (3300)/x and the time it takes the sound to get back to you after hitting the target its (1100)/x. So the total time of 1/1.5 = (3300)/x + (1100)/x = (4400)/x so x = (4400)*1.5 = 6600 meters


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stan
guest
Nov-15-04, 04:02 PM (EST)
 
7. "RE: Bullet Sound"
In response to message #1
 
   while I do not disagree with the solutions provided, I wonder what kind of bullet travels at 3300 m/s? (~ 2 miles per second!)

Furthermore, the speed of sound in air is about 330 m/s I think. It may be 1100 m/s in some solids or liquids, but then that would radically change the question!

regards


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ry
guest
Nov-17-04, 10:00 AM (EST)
 
8. "RE: Bullet Sound"
In response to message #1
 
   >The time it takes to get to the target that is x meters away is (3300)/x

No, the time it takes to get to the target is x/3300.


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Airborne Bob
guest
Oct-04-04, 01:40 PM (EST)
 
2. "RE: Bullet Sound"
In response to message #0
 
   Bullet travels to target in time t1 = d/rb (rate of bullet)
where rb = 3300 ft/s
Sound travels from target to observer in time t2 = d/rs (rate of sound)
where rs = 1100 ft/s
Total time is 1.5 sec, so d/3300 + d/1100 = 1.5
multiply everything by 1100 (to get rid of d/1100) gives
d/3 + d = 1650
multiply everything by 3 (to get rid of d/3) gives
d + 3d = 4950 <--- d + 3d is actually 1d + 3d, so
4d = 4950
divide by 4 to get d by itself gives us
d = 4950/4
d = 1237.5ft

Check your answers:
t1 = 1237.5/3300 = 0.375 sec
t2 = 1237.5/1100 = 1.125 sec
add the times and -----
you should get 1.5 sec


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ECON
guest
Oct-07-04, 10:09 AM (EST)
 
3. "RE: Bullet Sound"
In response to message #0
 
   You can only start hearing the bullet hit the target when it did indeed hit the target. So you do not need to calculate the time that it takes (nor the distance) for the bullet to hit the target. You only need to now that at the time the target is hit, the sounds starts to travel back to you.

So according to me, the target is 1650 meters away (1100 m/s * 1,5 s).


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rewboss
guest
Oct-08-04, 10:19 AM (EST)
 
4. "RE: Bullet Sound"
In response to message #3
 
   >You can only start hearing the bullet hit the target when it
>did indeed hit the target. So you do not need to calculate
>the time that it takes (nor the distance) for the bullet to
>hit the target. You only need to now that at the time the
>target is hit, the sounds starts to travel back to you.

No, because the sound is heard 1.5 seconds after the gun is fired, not 1.5 seconds after the bullet hits the target. That means that the 1.5 seconds includes the time it took for the bullet to travel from the gun to the target.

The events, in order, are:

Bullet is fired from gun. Stopwatch starts.
Bullet travels to target.
Bullet hits target.
Sound of bullet hitting target travels back to marksman.
Marksman hears sound of impact, stops stopwatch at 1.5 seconds.


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ECON
guest
Oct-12-04, 09:35 AM (EST)
 
5. "RE: Bullet Sound"
In response to message #4
 
   I see my mistake. The question was indeed posted otherwise. Given that, the solution is indeed 1237.5 meters.

Calculation. The bullet travels 3 times faster than the sound. Therefore 1/(1+3) of the time is spent for the bullet to travel to the target and 3/(1+3) of the time is spent to the sound travelling back.
Thus, for the bullet: 1/4 * 1.5 sec * 3300 meters/sec = 1237.5 meters
Idem for the sound: 3/4 * 1.5 sec * 1100 meters/sec = 1237.5 meters


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Airborne Bob
guest
Oct-13-04, 01:17 PM (EST)
 
6. "RE: Bullet Sound"
In response to message #5
 
   Not a problem, friend.
Word problems are like that - which is why students hate them so!


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lokesh gupta
guest
Nov-20-04, 10:38 AM (EST)
 
9. "RE: Bullet Sound"
In response to message #0
 
   4950/4= 1237.50 m is the distance of the target


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