A climber stands on a ledge on one side of a valley. He claps his hands and hears an echo from

the opposite side of the valley 1.6 s later. How wide is the valley?

d = V*t = 343m/s * (1.6s/2) = 274.4 m.

To calculate the width of the valley, we need to determine the time it takes for the sound to travel from the climber to the opposite side and back.

Here's how we can get the answer:

1. Since the time it takes for the sound to go to the opposite side of the valley and come back is 1.6 seconds, we can split it into two equal parts. So, the time it takes for the sound to reach the opposite side is 0.8 seconds.

2. The speed of sound in air is approximately 343 meters per second (at room temperature). We can use this value to calculate the distance traveled by the sound.

3. By multiplying the speed of sound (343 m/s) by the time it takes for the sound to reach the opposite side (0.8 s), we can find the distance traveled by the sound in one direction.

Distance = Speed * Time
Distance = 343 m/s * 0.8 s
Distance = 274.4 meters

4. Since the sound travels that distance one way, to find the total width of the valley, we multiply the distance by 2 because it must travel from the climber to the opposite side and back.

Total Width = 2 * Distance
Total Width = 2 * 274.4 meters
Total Width = 548.8 meters

Therefore, the width of the valley is approximately 548.8 meters.