Question

Imagine an old hermit living in a cave in the mountains. Just before going to sleep, he yells “WAKE UP!” The sound echoes o↵ the nearest mountain and returns 8.5 hours later. Find the distance to the mountain. Sketch a diagram to clarify your analysis.

Answer 1

According to the given probelm,

Since distance equals rate times time, we use
D = v * t
where rate v is the speed of sound (343 meters/second), and the distance D traveled is twice the distance to the mountain M.

We convert the 8.5 hours into seconds using
8.5 hours * (60 minutes / 1hour) * (60 seconds/1 minute) = 30,600 seconds

(2 * M) = 343m/s * 30,600 seconds
so
M = 5.25*10⁶ m = 5248 km

So the distance to the mountain is 5248 km.

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