how to calculate a distance when sound is involved?

Question

if lets say a arrow is shot, the target is 50 meters away and the sound of the arrow hiting the target is heard 1.5 s after the arrow was fired. and the speed of sound is 340 m/s how do i calculate how fast the arrow was travelling?

Answer 1

Distance travelled by the arrow , Da= 50 m
Velocity of Sound Vs = 340 m/sec
Time of arrow, Ta
Time of souns, Ts
Total time from the arrow is released until it was heard back, 1.5 seconds

Velocity of arrow Va = REQUIRED
Working equation Velocity = distance / time
Va = Da/Ta

So;
Ta + Ts = 1.5 sec
Ta = 1.5 sec - Ts (equation 1)

Va = Da / Ta (subtitute 1)
Va = Da / 1.5 sec - Ts (equation 2)

Solving for Ts;
1 sec/ 340 m x 50 m = 0.147 sec

Substitute to equation 2

Va = 50 m / (1.5 sec - 0.147 sec)
Va = 36.95 m / sec

Answer 2

it has been a long time for me, but lemme give this a shot.

first off, you need to determine how long it took for the sound alone to come back to you. you know that sound moves at 340 m/s, and it only needs to come back 50 m, which is about 1/7 of the needed time. (50/340=.147)

then, you would subtract the 0.147s from the 1.5 total seconds, and are left with 1.353 s it took the arrow to travel through the air

the arrow traveled 50 m in 1.353 seconds.. divide both sides by 1.353 to make the 'time' side equal 1. so it's 36.95 m/s

[the other answers reminded me that i had no reason to multiply the 1.5 and the .147]

Answer 3

well the arrow traveled 50 meters there, so the sound must travel 50 meters back.

So let's calculate the time it took for the sound to travel back, since we know it's speed.

1 s / 340 m * 50 m = 0.147 s

now we can subtract that value from the total time, to get the time it took for the arrow to reach the target.

1.5 - 0.147 = 1.353

So now we know that the arrow traveled 50 meters in 1.353 seconds, so by dividing these numbers: 50 / 1.353

you can determine that the arrow was travelling at approximately 36.95 m / s

Answer 4

If you are at the starting point where that arrow was launched
Time X Speed = Distance
1.5 X (Unknown) = 50
1.5/50
you take the known, in this case the Time the it took to travel 50 meters and divide by the distance. the time it takes the sound to travel is so negligible it's not worth calculating

Answer 5

340 divided by 3

Answer 6

You know the distance d= 50 m.
also the velocity of sound. Vs= 340 m/sec.
Calculate the time of sound Ts= 50 m /340 m/sec
Ts=0.147 sec.
Then time of the arrow Ta=1,5 sec - 0.147 sec =1.3529 sec.
Then velocity of arrow Va= 50 m / 1.3529 sec.= 36.9576 m/sec.
Va= 36.97 m/sec.

Answer 7

340 times 1.5

Answer 8

Good question...

It took .15 seconds for the sound to reach you when the target was hit (50M/340M/sec).

So the remaining 1.35 seconds are taken up by the arrow travelling.

Speed = 50M/1.35sec = 37.04 M/sec