SOLUTION: An airplane was flying over a city, when one engine stopped working. The airplane slowed down to 100 feet per second. Convert the speed of teh airplane to miles per hour to determi

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Question 513605: An airplane was flying over a city, when one engine stopped working. The airplane slowed down to 100 feet per second. Convert the speed of teh airplane to miles per hour to determine if it is going to crash.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
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This problem is mainly an exercise in converting from one set of units to another. Conversions require keeping the units organized so that all the units eventually cancel out except for the units you need. In this problem you want to go from feet per second to miles per hour. Here is a set of steps that will get you there:
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First write the units that you have given to you in the problem. In this case it is 100 feet per 1 second. The word "per" can be interpreted as "divided by".
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So we write this as:
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%28100ft%29%2F%281sec%29
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Next we need to multiply this by some conversion factors. We can begin by changing the units of feet (ft) to miles. We know that there are 5280 feet per 1 mile. For this conversion to take place we need to have the feet in the denominator so that the units of feet in the denominator will cancel with the units of feet in the numerator of 100 ft.We can do this by putting 5280 ft in the denominator and the 1 mi in the numerator. This results in:
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%28100ft%29%2F%281sec%29%29%2A%28%281mi%29%2F%285280ft%29%29
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Note that the units of ft will cancel out (just the units, not the numbers) and we are left with units of miles (mi) in the numerator and sec in the denominator. After cancelling the "ft" units out we have:
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%28%28100%29%2F%281sec%29%29%2A%28%281mi%29%2F%285280%29%29
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Since we are looking for an answer involving miles per hour which is mi%2Fhr we can note that we have the miles part in the numerator that we are looking for. So let's continue by working on converting the "seconds" in the denominator into "hours". We know that there are 60 seconds per 1 minute and we can write this as %28%2860sec%29%2F%281min%29%29. We know that this is the way we need to write this factor so that the units of seconds are in the numerator and will cancel with the unit of seconds in the denominator that we have. We can add this factor as follows:
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%28%28100%29%2F%281sec%29%29%2A%28%281mi%29%2F%285280%29%29%2A%28%2860sec%29%2F%281min%29%29
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And when we cancel the two units of sec, one in the numerator and one in the denominator this becomes:
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%28%28100%29%2F%281%29%29%2A%28%281mi%29%2F%285280%29%29%2A%28%2860%29%2F%281min%29%29
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So, the units we have left are miles (mi) and minutes (min). The miles is in the answer that we are trying to get, but we still need to get from minutes to hours. We know that there are 60 minutes per hour which can be written as:
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%28%2860min%29%2F%281hr%29%29
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Notice that this has the units "min" in the numerator so the units will cancel with the units of "min" in the denominator of our conversion. So put this conversion factor in, and our conversion becomes:
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Cancel out the units of "min" and we are left with:
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Notice that the units we have left are miles in the numerator, and hour in the denominator. This means that when we are done multiplying this out the units will be miles per hour. The multiplication will be:
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%28100%2A1%2A60%2A60%29%2F%281%2A5280%2A1%2A1%29
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Multiplying the numerator results in:
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%28360000%29%2F%281%2A5280%2A1%2A1%29
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And the denominator multiplies out to just 5280. So we are left with:
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360000%2F5280
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And when you divide this out the answer is 68.18181818. So the airplane's speed of 100 feet per second converts to a speed of 68.18 miles per hour. For a plane that normally has two engines driving it, this is pretty slow, and a likely result is that it will not be able to stay up.
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Hope this exercise helps you to understand an approach to making conversions by understanding how to analyze and use units to get from one set of given units to a set of units that you need.
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