A person fires an arrow at 46.9 m/s at a nearby target some distance away. The sound of the arrow striking the target returns to the person at a rate of 321.8 m/s. If the total elapsed time between the release of the arrow and the person hearing the thud of the arrow is 2.24 seconds, what is the distance between the person and the target in meters?
distance to target = d
arrow speed = 46.9 m/s
time arrow to target = d/46.9
speed sound back = 321.8 m/s
time sound coming back = d/321.8
so
2.24 = d/46.9 + d/321.8
your turn now.
Help a homie out guys
Thanks a lot dude!
I just didn't know how to get started
To find the distance between the person and the target, we can use the formula:
distance = speed * time
In this case, we have two different speeds involved: the speed of the arrow and the speed of sound. Let's break down the problem step by step.
Step 1: Calculate the time it takes for the arrow to reach the target.
We know that the speed of the arrow is 46.9 m/s. Let's assume it takes time "t" for the arrow to reach the target.
distance (arrow) = speed (arrow) * time (arrow)
Since we're looking for the distance the arrow travels, we can rewrite this as:
distance (arrow) = 46.9 m/s * t
Step 2: Calculate the time it takes for the sound to travel back to the person.
We know that the speed of sound is 321.8 m/s. Since the sound has to travel twice the distance between the person and the target, the time it takes for the sound to reach the person will be twice the time it took for the arrow to reach the target. So, the time for the sound is "2t".
Step 3: Calculate the total time elapsed.
The problem states that the total elapsed time between the release of the arrow and the person hearing the thud of the arrow is 2.24 seconds. This includes the time it takes for the arrow to reach the target ("t") and the time for the sound to travel back to the person ("2t"). So we can write the equation:
t + 2t = 2.24 seconds
Simplifying, we have:
3t = 2.24 seconds
Step 4: Solve for "t".
Divide both sides of the equation by 3:
t = 2.24 seconds / 3
t ≈ 0.7467 seconds
Step 5: Calculate the distance between the person and the target.
Now that we know the time it took for the arrow to reach the target (approximately 0.7467 seconds), we can calculate the distance:
distance (arrow) = 46.9 m/s * 0.7467 seconds
distance (arrow) ≈ 34.989 m
Therefore, the distance between the person and the target is approximately 34.989 meters.