Question

4: if you shout into grand canyon, your voice travels at the speed of sound (340 m/s) to the bottom of the canyon and back, and you hear an echo. how deep is the grand canyon in a spot where you can hear your echo 5.2 seconds after you shout?

Explanation:

Step1: Determine total distance sound travels

The sound travels to the bottom of the canyon and back. The time taken for this round - trip is $t = 5.2$ s and the speed of sound $v=340$ m/s. Using the formula $d = v\times t$, the total distance $d$ the sound travels is $d = 340\times5.2$ m.

Step2: Calculate depth of canyon

The total distance $d$ is the distance to the bottom and back. Let the depth of the canyon be $h$. Then $d = 2h$. So, $h=\frac{d}{2}$. Substituting $d = 340\times5.2$ into the formula for $h$, we get $h=\frac{340\times5.2}{2}$ m.
$h = 340\times2.6=884$ m

Answer:

884 m