Question

Sound travels about 750 miles per hour. If you stand in a canyonand sound a horn, you will hear an echo.Suppose it takes about 4 seconds to hear the echo. How far awayis the canyon wall, in feet?distancefeetNow let's generalize that result. Suppose it takes n seconds tohear the echo. How far away is the canyon wall, in terms of n?distancefeet

Answer 1

Answer:

distance: 2200 ft

distance: 550n ft

Explanation:

First, we need to convert 750 miles per hour into feet per second.

Since 1 mile = 5280 feet and 1 hour = 3600 seconds, we get:

$750\text{miles}/\text{hour}\times\frac{5280ft}{1mile}\times\frac{1h}{3600s}=1100ft/s$

Then, the distance can be calculated as the velocity times time.

It takes about 4 seconds to hear the echo, so it reaches the canyon wall after half of this time. It means that the distance is equal to

$\begin{gathered} \text{distance = velocity }\times time \\ \text{distance}=1100ft/s\times\frac{4s}{2} \\ \text{distance = 2200 ft} \end{gathered}$

If it takes n seconds to hear the echo, the time will be n/2 seconds, so the distance will be

$\begin{gathered} \text{distance}=1100\times\frac{n}{2} \\ \text{distance}=550n \end{gathered}$

Therefore, the answers are:

distance: 2200 ft

distance: 550n ft