Question 403256
one key is to pick unit entities (by "unit" I mean "1") to cancel out the units you don't want and give you the units you DO want. 


key point: anything divided by the same thing is equal to 1; so an example of a "unit" entity would be {1 cup / 8 ounces} or {8 ounces / 1 cup} or {12 inches / 1 foot} or {1 foot / 12 inches} - - - - ALL unit entities are equal to "1"


anything "multiplied by one" is equal to that same thing - - > so anything times a {unit entity} is that "same thing", just maybe expressed in different terms; for example, 12 inches is the same as 1 foot (same thing but expressed in different terms)



The terms we start with  ==> miles per hour


The terms we want to end with  ==> feet per second


So to end up with feet per second we pick unit entities to "multiply by one" until we have the term we want


if a term you want to eliminate is in the numerator the unit entity you pick must have that term in the denominator


if a term you want to eliminate is in the denominator then the unit entity you pick must have that term in the numerator


that process is called unit-cancellation, and it helps you end up with the units you want


also if x/y = 1, then it is also true that y/x = 1, so you are free to invert a unit entity, or an answer and still get a true result, but in the terms you want to see


We use the above principles to solve the problem now, step by step:


I don't want hours in my units, I want seconds; and 1 hour is the same as 3600 seconds because there are 60 seconds in every minute and also 60 minutes in every hour and 60 times 60 = 3600
(200 miles / hour) * {1 hour / 3600 seconds} = 0.0555 miles per second


I don't want miles in my units, I want feet; and 1 mile is the same as 5280 feet
(0.0555 miles / second)* {5280 feet / 1 mile} 


= 293.33 feet / second, or

293.33 feet per second