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

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) (Show Source): You can put this solution on YOUR website!
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
+ = 2 sec
:
The observer equation (bullet is traveling while rifle report is traveling)
+ - = 1
:
+ = 1
:
Use elimination here
+ = 2
+ = 1
--------------------------------subtraction eliminates v, find s
= 1
s = 350 m/sec is the speed of sound
:
Find v
+ = 1
+ = 1
Multiply by 5v
v + 5(420) = 5v
2100 = 5v - v
2100 = 4v
v =
v = 525 m/sec is the bullet velocity
:
:
Confirm these values in the Marksman equation
+ =
.8 + 1.2 = 2 sec
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