A rifle with a muzzle velocity of 1170. m/s is fired at a target that is 600. m away. If the
speed of sound in air is 340. m/s, how long after the shot strikes the target will the sound of the
rifle firing reach the target?
To find out how long it will take for the sound to reach the target after the shot strikes it, we need to calculate the time it takes for the bullet to reach the target and then subtract the time it takes for sound to travel the same distance.
First, let's calculate the time it takes for the bullet to reach the target:
Distance = Speed × Time
600 m = 1170 m/s × Time (let's call this Time1)
Now, let's calculate the time it takes for the sound to travel the same distance:
Distance = Speed × Time
600 m = 340 m/s × Time (let's call this Time2)
Now we have two equations:
600 m = 1170 m/s × Time1
600 m = 340 m/s × Time2
Now, let's solve these equations to find Time1 and Time2. Starting with Time1:
Time1 = 600 m / 1170 m/s
Time1 ≈ 0.513 seconds
Now, solving for Time2:
Time2 = 600 m / 340 m/s
Time2 ≈ 1.765 seconds
Since we are interested in finding out how long after the shot strikes the target the sound reaches it, we need to subtract Time1 from Time2:
Time after the shot strikes the target = Time2 - Time1
Time after the shot strikes the target ≈ 1.765 seconds - 0.513 seconds
Time after the shot strikes the target ≈ 1.252 seconds
Therefore, it will take approximately 1.252 seconds for the sound of the rifle firing to reach the target after the shot strikes it.