How do you convert 56 miles per hour to feet per second?

Answer 1

Via the Factor Label Method.

The best way to convert units is the factor label method. First, write the fraction out:

56 mi./1 hr.

Whatever is happening is at a rate of 56 miles in every 1 hour. Next, we need to convert miles to feet and hours per second. Multiply the original fraction by the proportion which these units are in to each other. The units, like hours, should be able to cancel from top to bottom, like variables in fractions, leaving you with the unit you converted to. For instance, in one hour there are 3600 seconds. So, we'll be using the fraction 1 hour/3600 seconds, and multiplying it by the original. Since there is an hour in the numerator and one in the denominator, they will cancel, leaving the desired unit, seconds.

56 mi./1 hr. x 1 hr./3600 s

We could multiply these, but it's easier to multiply everything out at once, so lets add out next fraction onto this. There are 5280 feet in a mile. By multiplying 56 mi./1 hr. and 5280 ft./ 1 mi., we can see that the mile in the numerator will cancel with the mile in the denominator, leaving out desired unit.

Now, let's calculate to find the answer.

56 mi./1 hr. x 1 hr./3600 s x 5280 ft./ 1 mi. = 82.1333333333

But wait! We're not done yet. How can we have more digits than we started with in the information used? Since an answer is taken from the information given, if it has any more digits, those digits are not taken from actual data, and thus the answer must be shortened to the least amount of digits in the information given. 1 hour, technically, is 1.000000, etc., repeating infinitely. 56 miles was measured, however, so that limits us to 2 digits. Thus, the answer is 82 ft./1 s: 82 feet per second.