Question

A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than to the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 2.1 s after the first, and the third echo arrives 0.5 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the distance between the cliffs. 445.9 Incorrect: Your answer is incorrect. m

1. thanhha

531.65 m

Explanation:

Let d₁ be the distance between the hunter and the closer cliff and d₂ be the distance between the hunter and the farther cliff. The speed of sound v = 343 m/s.

t₁ is the time taken for the sound to reach the neared cliff and return back to the hunter as echo. Hence:

t₁ = 2d₁/343

t₂ is the time taken for the sound to reach the farther cliff and return back to the hunter as echo. Hence:

t₂ = 2d₂/343

t₂ – t₁ = 2.1

2d₂/343 – 2d₁/343 = 2.1

d₂ – d₁ = 360.15        (2)

t₃ is the time taken by the third echo as a result of the second echo reaching the nearer cliff. Hence:

t₃ = 2d₁/343

0.5 = 2d₁/343

d₁ = 85.75 m

d₂ – d₁ = 360.15

d₂ – 85.75 = 360.15

d₂ = 445.9 m

The distance between the two cliffs = d₁ + d₂ = 445.9 + 85.75 = 531.65 m