An archer fires an arrow, which produces a muffled "thwok" sound after it hits a target. The archer hears the "thwok" exactly 2.6 s after firing the arrow and the average speed of the arrow is 36 m/s. Find the distance separating the archer and the target? Use 340 m/ s for the speed of sound.
i cannot find a good explanation of how to go about this problem. i am at a total loss as to what to do.
To solve this problem, we need to understand that the time it takes for the sound of the "thwok" to reach the archer is the total time that the arrow takes to travel to the target plus the time it takes for the sound to return.
Let's break down the problem:
1. The time it takes for the sound to reach the archer is given: 2.6 seconds.
2. The average speed of the arrow is given: 36 m/s.
3. The speed of sound is given: 340 m/s.
To find the distance separating the archer and the target, we can consider the time it takes for the sound to reach the archer and work backward.
Let's denote the distance between the archer and the target as "d."
1. The time it takes for the arrow to reach the target is the distance divided by the average speed of the arrow: t1 = d / 36 m/s.
2. The time it takes for the sound to return to the archer is the distance divided by the speed of sound: t2 = d / 340 m/s.
3. The total time it takes for the sound to reach the archer is the sum of t1 and t2: t1 + t2 = 2.6 s.
Now we can set up the equation:
t1 + t2 = 2.6 s
d / 36 m/s + d / 340 m/s = 2.6 s
To solve for "d," we'll need to combine the fractions:
(340d + 36d) / (36 * 340) m/s = 2.6 s
Simplifying further:
376d / 12240 m/s = 2.6 s
Now, we can isolate "d" by multiplying both sides of the equation by the speed of sound:
d = (2.6 s) * (12240 m/s) / 376
Evaluating the expression:
d ≈ 84.47 meters
So, the distance separating the archer and the target is approximately 84.47 meters.
time = distance / rate
(d / 36) + (d / 340) = 2.6