you are in a canyon and yell across. it takes 4 seconds it takes 4 seconds for the echo to come back how wide is the canyon?

To determine the width of the canyon using the time it takes for an echo to return, we can make use of the speed of sound. The speed of sound varies depending on factors such as temperature and humidity, but for approximate calculations, it is commonly considered to be around 343 meters per second (or 1125 feet per second) in dry air at room temperature.

Now, let's break down the process of determining the width of the canyon using the given information:

1. Firstly, we need to consider the time it takes for the sound to travel from one side of the canyon to the other and back as an echo. In this case, it took 4 seconds for the echo to return.

2. To find the total distance traveled by sound, we need to consider that the sound traveled to the other side of the canyon and then back to the original location. This distance is equal to twice the width of the canyon.

3. Using the formula: distance = speed × time, we can calculate the total distance traveled by the sound using the speed of sound.

distance = speed of sound × time
= 343 m/s × 4 s
= 1372 meters (or 4500 feet)

4. Since the distance obtained is twice the width of the canyon, we can determine the width by dividing this value by 2.

width of the canyon = distance / 2
= 1372 meters / 2
= 686 meters (or 2250 feet)

Therefore, based on the given information, the width of the canyon is approximately 686 meters (or 2250 feet).