Question

a person stamding at a distance x in front of a cliff fires a gun. another person be standing behind the person a at distance y from the Cliff hears two sounds of the fired shot after 2 seconds and 3 seconds respectively calculate x and y (take speed of sound 320 metre per second)
answer is x=160m and y=800m​

Answer 1

Explanation:

The first sound the person will hear comes directly from the gun.

The second sound they hear is the sound from the gun echoing back from the cliff, meaning the sound travels all the way to the cliff and back to their ears.

1. The first sound, then, covers distance a, as shown in the diagram. We know that it takes 2 seconds for the sound to travel this distance.

We also know that $speed=\frac{distance}{time}$, so if we want to solve for distance we can multiply both sides by time to get $distance=speed*time$. If we plug in our known values of 2 seconds for time and $320m/s$ for speed, we get that the distance is $640m$.

$640m$ is the distance between the two people, which doesn't actually answer the question. However, it does tell us their relative positions, so if we can find one person's position we can find the other's with ease.

The question tells us that the person listening is $y$ metres from the cliff, and the person shooting is $x$ metres from the cliff. $y$ should be greater than $x$, so we can say that $y=x+480$.

2. The second sound takes longer, meaning that's the sound that went to the cliff and back to the person listening. The sound traveled distance b towards the cliff, and then distance c as it traveled back towards the person listening.

From this information, we can say that the distance traveled by the second sound is equal to the sum of distance b and c. We also know that it took three seconds to cover this distance.

If we use our distance equation again, we get that distances a and c were a total of $960m$. Looking at the diagram, we can break down distance c into the sum of distances a and b. Now, we can say that the sound traveled distance b once towards the cliff, once again away from the cliff, and then traveled distance a back towards the listener. Since this distance is now known to be $960m$, we can say that $960=a+b+b$, or $960=2b+a[tex]. </p><p></p><p>We know from the first part that distance <strong>a</strong> is [tex]640m$, which we can plug into our new equation:

$960=2b+640$

If you subtract 640 from both sides, you get that

$320=2b$

$160=b$

If we refer back to the image, we see that distance b is how far the person shooting is from the cliff, and distance c is how far the person listening is from the cliff. We also know that distance c is just distances a and b added up.

From all this, we can say that the person shooting is $160m$ from the wall ($x$), and the person listening is $160m+640m$ or $800m$ from the wall ($y$).

Answer 2

Answer:

The person B hears two of the fired shots , the first one is direct from the gun while other sound comes after reflection from the cliff

 

Speed of sound 320m/s

Time taken by the sound to reach from A to B directly