An archer fires an arrow, which produces a muffled "thwok" as it hits a target. if the archer hears the "thwok" exactly 1 s after firing the arrow and the average speed of the arrow was 40 mis, what was the distance separating the archer and the target? use 340 m/ s for the speed of sound.

35,79 meters

Explanation:

So, we got an archer, and we got a target. Lets call the distance between this two d.

Now, the archer fires the arrow, that, in a time travels the distance d with a speed of 40 m/s and hits the target. We can see that the equation will be:

Immediately after this, the arrow produces a muffled sound, which will travel the distance d at  340 m/s in a time . Obtaining :

.

Finally, the sound reaches the archer, exactly 1 second after he fired the bow, so:

.

This equation allows us to write:

.

Plugging this  relationship in the distance equation for the sound:

.

Now, we can replace d from the first equation, and obtain:

.

Now, we can just work a little bit:

.

Now, we can just plug this value into the first equation: