If you shout into the Grand Canyon,your voice travels at the speed of sound(340 m/s) to the bottom of the canyon and back,and you hear and echo.How deep is the canyon at a spot where you can hear your echo 5.2 seconds after you shout.

if depth is d, signal goes 2 d (down and up)

2 d = 340 t = 340 * 5.2
d = 170 * 5.2 meters

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Does really work

To determine the depth of the canyon at a spot where you can hear your echo 5.2 seconds after shouting, we can use the equation:

Distance = (Speed of sound x Time) / 2

Since the sound travels down to the bottom of the canyon and then back up, the total distance covered is twice the canyon depth.

Therefore, the equation becomes:

2 x Distance = (Speed of sound x Time)

Plugging in the given values:

2 x Distance = (340 m/s x 5.2 s)

Simplifying the equation:

2 x Distance = 1768 m

Finally, solving for Distance (canyon depth):

Distance = 1768 m / 2

Distance = 884 m

Hence, the depth of the canyon at a spot where you can hear your echo 5.2 seconds after shouting is 884 meters.