Question

sound travels about 750 miles per hour. if you stand in a canyon and sound a horn, you will hear an echo. round your answers to the nearest tenth as needed. a) suppose it takes about 3 seconds to hear the echo. how far away is the canyon wall, in feet? the canyon wall is feet away. b) suppose you stand 1,375 feet from the canyon wall and sound the horn. how long will it take to hear the echo? it will take seconds to hear the echo. question help: video message instructor submit question jump to answer

Explanation:

Step1: Convert speed to feet - per - second

First, convert 750 miles per hour to feet per second. 1 mile = 5280 feet and 1 hour = 3600 seconds. So the speed $v$ in feet per second is $v=\frac{750\times5280}{3600}=1100$ feet per second.

Step2: Solve part a

The sound travels to the canyon wall and back in 3 seconds. Let the distance to the wall be $d$. The total distance traveled by sound is $2d$ (to the wall and back). Using the formula $d = vt$, where $t$ is the one - way time. Since the total time $T = 3$ seconds, the one - way time $t=\frac{3}{2}=1.5$ seconds. Then $d=1100\times1.5 = 1650$ feet.

Step3: Solve part b

The total distance the sound travels for the echo is $2d$, where $d = 1375$ feet, so the total distance $D=2\times1375 = 2750$ feet. Using the formula $t=\frac{D}{v}$, with $v = 1100$ feet per second, we get $t=\frac{2750}{1100}=2.5$ seconds.

Answer:

a) 1650
b) 2.5