You are standing in a valley with parallel vertical walls when a rockslide occurs on side. You see the slide and its sound 2.2 seconds later, then the echo from the other wall heard 3.5 sec later. What is the width of the valley?
To find the width of the valley, we need to analyze the time it takes for the sound to travel and bounce back from each wall.
First, we should consider the time it takes for the sound of the rockslide to reach you. You mentioned that you hear the sound of the rockslide 2.2 seconds after seeing the slide. This delay is the time it takes for the sound to travel from the rockslide to your location.
Next, we need to calculate the time it takes for the sound to travel from your location to the wall opposite to the rockslide and bounce back as an echo. According to the problem, this echo is heard 3.5 seconds after hearing the rockslide sound.
Now, let's break down the time travel and echo:
1. Time for the rockslide sound to reach you: 2.2 seconds
2. Time for the sound to travel from your location to the opposite wall: This is the same as the time it takes for the echo to return from the opposite wall to your location.
3. Time for the echo to reach you: 3.5 seconds
To find the width of the valley, we need to find the total time it takes for the sound to travel from the rockslide to the opposite wall and back to your location. We can calculate this by subtracting the time of the rockslide sound, the time for the echo, and twice the time for the sound to travel from your location to the opposite wall:
Total time = Time for rockslide sound + Time for echo + 2 * Time for sound to travel from your location to opposite wall
Total time = 2.2 s + 3.5 s + 2 * Time for sound to travel from your location to opposite wall
Now, since the speeds of sound traveling to the opposite wall and back are the same, we can assume they cancel each other out. Therefore, we only need to consider the time it takes for sound to travel from your location to the opposite wall:
Total time = 2.2 s + 3.5 s + 2 * Time for sound to travel from your location to opposite wall
Total time = 5.7 s + 2 * Time for sound to travel from your location to opposite wall
Now, if we subtract the known time intervals (rockslide sound and echo) from the total time, we can isolate the time it took for the sound to travel from your location to the opposite wall:
Time for sound to travel from your location to opposite wall = Total time - (Time for rockslide sound + Time for echo)
Time for sound to travel from your location to opposite wall = 5.7 s - (2.2 s + 3.5 s)
After calculating this expression, you will get the time it took for the sound to travel from your location to the opposite wall. Since the speed of sound is approximately 343 meters per second, you can multiply the time by the speed of sound to find the width of the valley:
Width of valley = Time for sound to travel from your location to opposite wall * Speed of sound (approximately 343 m/s)
By solving this equation, you will find the width of the valley.