SOLUTION: A marksman fires at a target 420 meters away and hears the bullet strike 2 seconds after he pulled the trigger. An observer 525 meters away from the target and 455 meters from the

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Question 346028: A marksman fires at a target 420 meters away and hears the bullet strike 2 seconds after he pulled the trigger. An observer 525 meters away from the target and 455 meters from the marks man hears the bullet strike the target 1 second after he hears the report of the rifle. Find the velocity of the bullet and the velocity of the sound.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A marksman fires at a target 420 meters away and hears the bullet strike 2
seconds after he pulled the trigger.
An observer 525 meters away from the target and 455 meters from the marksman
hears the bullet strike the target 1 second after he hears the report of the rifle.
Find the velocity of the bullet and the velocity of the sound.
:
Let s = speed of sound
Let v = velocity of the bullet
:
The Marksman equation
420%2Fv + 420%2Fs = 2 sec
:
The observer equation (bullet is traveling while rifle report is traveling)
525%2Fs + 420%2Fv - 455%2Fs = 1
:
70%2Fs + 420%2Fv = 1
:
Use elimination here
420%2Fv + 420%2Fs = 2
420%2Fv + 70%2Fs = 1
--------------------------------subtraction eliminates v, find s
350%2Fs = 1
s = 350 m/sec is the speed of sound
:
Find v
70%2F350 + 420%2Fv = 1
1%2F5 + 420%2Fv = 1
Multiply by 5v
v + 5(420) = 5v
2100 = 5v - v
2100 = 4v
v = 2100%2Fv
v = 525 m/sec is the bullet velocity
:
:
Confirm these values in the Marksman equation
420%2F525 + 420%2F350 =
.8 + 1.2 = 2 sec