Question

A group of hikers hear an echo 4.50 s after they shout. if the temperature is 20.0degrees celsius, how far away is the mountain?

Answer 1

The mountain is approximately 386.175 meters away from the hikers, calculated by using the speed of sound at 20.0 degrees Celsius and the time it took to hear the echo.

Step-by-step explanation:

The question is asking how far away a mountain is if hikers hear an echo after 4.50 seconds at a temperature of 20.0 degrees Celsius. The speed of sound at this temperature is approximately 343 meters per second (m/s). To find the distance the sound traveled, we multiply the speed of sound by the time it took to hear the echo and then divide by two, because the sound has to travel to the mountain and back. Thus, the calculation we need is:

Distance = (Speed of Sound) × (Time of Echo) / 2

Therefore:

Distance = 343 m/s × 4.50 s / 2 = 772.35 m

But this is the total distance sound traveled back and forth. The actual distance to the mountain is half of this value:

Distance to the mountain = 772.35 m / 2 = 386.175 m

So the mountain is approximately 386.175 meters away from the hikers.