An archer fires an arrow, which produces a muffled "thwok" sound after it hits a target. The archer hears the "thwok" exactly 3.0 s after firing the arrow and the average speed of the arrow is 32 m/s. Find the distance separating the archer and the target? Use 340 m/ s for the speed of sound.
time = distance / velocity
(distance / arrow speed) + (distance / sound speed) = 3.0
To find the distance separating the archer and the target, we need to consider the time it took for the sound to travel from the target to the archer.
Given:
- Speed of sound = 340 m/s
- Time taken for the archer to hear the sound = 3.0 s
- Average speed of the arrow = 32 m/s
First, let's calculate the distance traveled by the arrow:
The average speed of the arrow is given as 32 m/s, and the time for the arrow to reach the target is the same as the time for the sound to travel back to the archer. Therefore, distance = average speed × time taken.
Distance = 32 m/s × 3.0 s = 96 m.
Now, let's calculate the distance traveled by the sound:
Since the sound takes 3.0 s to reach the archer after hitting the target, and the speed of sound is 340 m/s, we can calculate:
Distance = speed of sound × time taken = 340 m/s × 3.0 s = 1020 m.
The total distance separating the archer and the target is the sum of the distance traveled by the arrow and the distance traveled by the sound:
Total distance = distance traveled by arrow + distance traveled by sound
Total distance = 96 m + 1020 m = 1116 m.
Therefore, the distance separating the archer and the target is 1116 m.