word problem: if speed is 30 kph, how many meters per sec?
- Thread starter chadcas
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Re: word problem
Have you heard of "Dimensional Analysis"? Some folks call it "Multiplying things by one (1)." That really is al that is being done.
\(\displaystyle \frac{30\;km}{1\;h}*\frac{1000\;m}{1\;km}*\frac{1\;h}{60\;min}*\frac{1\;min}{60\;sec}\;=\;\frac{30*100*1*1\;m}{1*1*60*60\;sec}*\frac{km}{km}*\frac{h}{h}*\frac{min}{min}\;=\)
All that is happening is the selection of units that will transform what one has into what one wants. In this case, I happen to know how many meters in a kilometer. For time, I suppose I could have used 3600 seconds per hour, but there is no harm in getting there in multiple steps.
Notice how the units all go away, excepting the ones you want. Multiply numerators and denominators and you're done.
Notice how the three factors I add are EXACTLY one (1) - just different ways of saying the same thing.
This is an excellent example of the loose definition of "word problem". Most problems have "words", don't they? i never understood why the concept strikes fear in the minds of so many. I'm not saying you are fearing this one, just that is does happen rather often.chadcas said:
Have you heard of "Dimensional Analysis"? Some folks call it "Multiplying things by one (1)." That really is al that is being done.
\(\displaystyle \frac{30\;km}{1\;h}*\frac{1000\;m}{1\;km}*\frac{1\;h}{60\;min}*\frac{1\;min}{60\;sec}\;=\;\frac{30*100*1*1\;m}{1*1*60*60\;sec}*\frac{km}{km}*\frac{h}{h}*\frac{min}{min}\;=\)
All that is happening is the selection of units that will transform what one has into what one wants. In this case, I happen to know how many meters in a kilometer. For time, I suppose I could have used 3600 seconds per hour, but there is no harm in getting there in multiple steps.
Notice how the units all go away, excepting the ones you want. Multiply numerators and denominators and you're done.
Notice how the three factors I add are EXACTLY one (1) - just different ways of saying the same thing.
Here's any easy way for converting:
http://tinyurl.com/5gap7j
But, make you sure you understand the math behind this (which tkhunny so elaborately explained for you) first! May i make a remark, Denis: your "i" should be capitalized! - I'm still not sure whether you did it on purpose or not though...
http://tinyurl.com/5gap7j
But, make you sure you understand the math behind this (which tkhunny so elaborately explained for you) first! May i make a remark, Denis: your "i" should be capitalized! - I'm still not sure whether you did it on purpose or not though...