Answer:
851 m
Explanation:
Let's say the distance to one mountain is x, and the distance to the other mountain is y, such that x < y.
First, the wave moves a distance x, reflects off the nearer mountain, and travels another distance x back to the boy. This is the first echo. The time is:
t₁ = 2x / c
Meanwhile, the wave also moves a distance y in the opposite direction, reflects off the further mountain, and travels another distance y back to the boy. This is the second echo. The time is:
t₂ = 2y / c
Finally, each wave reflects off the opposite mountain and travels a total distance of 2x + 2y. This is the third echo. The time is:
t₃ = (2x + 2y) / c
Which means:
t₃ = t₁ + t₂
We are given the differences between the times:
t₂ − t₁ = 1.92 s
t₃ − t₂ = 1.47 s
Since t₃ = t₁ + t₂:
t₁ + t₂ − t₂ = 1.47 s
t₁ = 1.47 s
Which means:
t₂ − 1.47 s = 1.92 s
t₂ = 3.39 s
And:
t₃ = 1.47 s + 3.39 s
t₃ = 4.86 s
Therefore:
4.86 = (2x + 2y) / c
4.86c = 2x + 2y
2.43c = x + y
Given c = 350 m/s:
x + y = (2.43 s) (350 m/s)
x + y = 850.5 m
Rounding to three significant figures, the distance between the mountains is 851 m.
