Hans stands at the rim of the Grand Canyon and yells down to the bottom. He hears his yell echo back from the canyon floor 4 .8 seconds later. How deep is the canyon?(Hint: An echo is heard in twice the time it takes sound to reach the canyon floor) A 892 m B 823 m C 1784 m D 1646 m

## Step 1<br />The problem involves the concept of echo and the speed of sound. An echo is a sound that is reflected off a surface and heard again. The time it takes for the echo to be heard is twice the time it takes for the sound to reach the surface. This is because the sound has to travel to the surface and then back again.<br /><br />## Step 2<br />The speed of sound in air is approximately 343 meters per second. This is a standard value used in physics problems.<br /><br />## Step 3<br />The total time for the sound to travel to the canyon floor and back is given as 4.8 seconds. However, since the sound has to travel to the floor and back, we need to divide this time by 2 to get the time it takes for the sound to reach the floor.<br /><br />### \( \text{Time to reach the floor} = \frac{4.8 \text{ seconds}}{2} = 2.4 \text{ seconds} \)<br /><br />## Step 4<br />Now, we can calculate the depth of the canyon by multiplying the time it takes for the sound to reach the floor by the speed of sound.<br /><br />### \( \text{Depth of the canyon} = \text{Time to reach the floor} \times \text{Speed of sound} \)<br />### \( \text{Depth of the canyon} = 2.4 \text{ seconds} \times 343 \text{ m/s} = 823.2 \text{ meters} \)