#17A1 please help me, thank you, will rate On a hiking trip, you are walking thr

Question

#17A1 please help me, thank you, will rate

On a hiking trip, you are walking through a canyon with vertical walls and are closer to one wall than the other. Having taken Physics, you decide to determine the width of the canyon by using your knowledge of kinematics and the speed of sound. You shout "Hey" as loud as you can, and after a short time you hear three echoes. The second echo arrives2.1 s after the first, and the third echo arrives 0.9 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 width of the canyon.
m

Explanation / Answer

let the width be W and you are at a distance of d from the wall closest to you

then the first echo you hear will be from the wall closer to you

hence time taken=2*d/v

where v is the speed of the sound

now the second echo will be from the wall farther than you

time taken by that echo will be 2*(W-d)/v

as we know second echo reaches 2.1 seconds after first,

2*(W-d)/v - 2*d/v=2.1

2*(W-2*d)=2.1*v....(1)

third echo will be the echo of the sound that comes from the second wall and hits the first wall.

so total distance travelled b this sound wave=2*(W-d)+2*d=2*W

then it is given that this echo reaches ou after 0.9 seconds of the second echo

so 2*W/v - 2*(W-d)/v =0.9

==> 2*d/v=0..9

d=0.9*v/2=154.35 m

then putting this value of d in equation 1, we get

W=668.85 m

hence the width of the canyon is 668.85 m

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