The speed of sound is 1,088 feet per second. Convert the speed of sound to miles per hour. Round your answer to the nearest whole number ? .

2 Answers
Feb 7, 2018

About 742 miles per hour, 741.bar81 to be exact

Explanation:

You can solve this by using dimensional analysis. Write what you have down:

1088 ft/ 1 sec

To use dimensional analysis, you want to get rid of the current units and end up with the next.
There are 5280 ft in a mile (mile because that is the unit you want to change to). Since you can only cross out something in the numerator with something in the denominator, you place 5280 ft in the denominator.

1088 ft/ 1 sec * 5280# ft

Since you cannot change the value of the equation, make sure to add 1 mile in the top.

1088 ft* 1 mi/ 1 sec * 5280 ft

1088cancel (ft) 1 mi/ #1 sec 5280#cancel (ft)

Now you have miles per second. Since you are looking for miles an hour, and the seconds are at the bottom, you need to add how many seconds in 1 hour in the numerator.
There are 3600 seconds in an hour.

1088* 1 mi * 3600 sec/ 1 sec *5280 *1 hr

The seconds cross out.

1088* 1 mi * 3600 cancel(sec)/ 1 cancel(sec) *5280 *1 hr

Multiply and get ~~742 mi / hr

Feb 8, 2018

The speed of sound in mi/h is 741.bar(18) "mi/h".

Explanation:

Use dimensional analysis. First write the equalities between feet and miles, and seconds and hours.

Feet to miles

"5280 ft"="1 mi"

Conversion factors

"5280 ft"/"1 mi" and "1 mi"/"5280 ft"

Seconds to hours

"3600 s"="1 h"

Conversion factors

"3600 s"/"1 h" and "1 h"/"3600 s"

Given

"1088 ft/s" rarr "? mi/h"

Multiply by the given speed by the conversion factors that cancel feet and seconds.

(1088color(red)cancel(color(black)("ft")))/(1color(blue)cancel(color(black)("s")))xx(1"mi")/(5280color(red)cancel(color(black)("ft")))xx(3600color(blue)cancel(color(black)("s")))/(1"h")=741.bar(18) "mi/h"