A bullet having a velocity of 680 m/s hits a target 510 m away. If the temp. of the air was 18 degrees celsius, how long after the bullet was fired did she hear it hit the target?

Figure two things

a) time it takes bullet to hit target: time=distanc/velocitybullet
b) time for sound to travel back to the shooter
time= distance/velocitysound

Add those two times.

To calculate the time it takes for the sound of the bullet hitting the target to reach the shooter, we need to use the speed of sound which depends on the temperature of the air.

The speed of sound in dry air can be approximated with the formula:

v = 331.4 + 0.6 * T

Where v is the speed of sound in meters per second (m/s) and T is the temperature in degrees Celsius.

Let's calculate the speed of sound at 18 degrees Celsius:
v = 331.4 + 0.6 * 18 = 342.2 m/s

Now, to find the time it takes for the sound to travel the distance between the shooter and the target, we can use the formula:

time = distance / speed

Given that the distance between the shooter and the target is 510 m, and the speed of sound is 342.2 m/s, we can calculate the time as follows:

time = 510 / 342.2 ≈ 1.49 seconds

So, approximately 1.49 seconds after the bullet was fired, the shooter would hear the sound of the bullet hitting the target.