A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than to the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 2.4 s after the first, and the third echo arrives 1.4 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the distance between the cliffs.

Question

A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than to the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 2.4 s after the first, and the third echo arrives 1.4 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the distance between the cliffs.

Answer 1

To solve this problem, we can use the fact that the speed of sound is a constant value of 343 m/s. We also know the time intervals between the echoes.

Let's break down the problem step by step:

Step 1: Determine the time it took for the first echo to reach the hunter.
Since the second echo arrived 2.4 seconds after the first, we can conclude that the first echo arrived 2.4 seconds before the second echo. So, we have:

Time for first echo = Time for second echo - Interval between the echoes
= 2.4 s - 2.4 s
= 0 s

This means the first echo arrived immediately after the gunshot.

Step 2: Determine the time it took for the second echo to reach the hunter.
Since the third echo arrived 1.4 seconds after the second, we can conclude that the second echo arrived 1.4 seconds before the third echo. So, we have:

Time for second echo = Time for third echo - Interval between the echoes
= 1.4 s - 1.4 s
= 0 s

This means the second echo arrived immediately after the first echo.

Step 3: Calculate the total time it took for all the echoes to come back.
The total time is the sum of the time intervals between the echoes:
Total time = Time for first echo + Time for second echo + Time for third echo
= 0 s + 0 s + Interval between the echoes
= 2.4 s + 1.4 s
= 3.8 s

Step 4: Calculate the distance traveled by sound.
Using the formula: distance = speed × time, we can find the distance traveled by sound.
Distance = Speed of sound × Total time
= 343 m/s × 3.8 s
= 1303.4 m

Step 5: Divide the distance by 2 to find the distance between the cliffs.
Since the sound travels from the hunter to one cliff and then from that cliff to the other, we can divide the total distance by 2 to find the distance between the cliffs.
Distance between the cliffs = Distance / 2
= 1303.4 m / 2
= 651.7 m

Therefore, the distance between the cliffs is approximately 651.7 meters.