Question

a runner ran 100 meters in 10.49 seconds. using dimensional analysis what is the miles per hour. my teacher said its 21.3 mph. How did she get that?

Answer 1

`\begin{gathered} (100)/(10.49)(m)/(s)\text{ we must convert meter to miles and seconds to hours.} \\ We\text{ know that} \\ 1\text{mile}=1609m \\ 1hr=3600\text{ s} \\ Fromtheserelations,y\text{ou can note that, } \\ (1mile)/(1609m)=1 \\ (3600s)/(1hr)=1 \\ \text{Then, we can apply the trick:} \\ (100)/(10.49)(m)/(s)=(100)/(10.49)(m)/(s)\cdot1\cdot1 \\ (100)/(10.49)(m)/(s)=(100)/(10.49)(m)/(s)((1mile)/(1609m))((3600s)/(1hr)) \\ (100)/(10.49)(m)/(s)=(100\cdot1\cdot3600)/(10.49\cdot1609\cdot1)\frac{\text{mile}}{\text{hr}} \\ (100)/(10.49)(m)/(s)=(360000)/(16878)\text{ }\frac{\text{mile}}{\text{hr}} \\ (100)/(10.49)(m)/(s)=21.3\text{ }\frac{\text{mile}}{\text{hr}} \\ \text{then te answer is} \\ 21.3\text{ }\frac{\text{mile}}{\text{hr}} \end{gathered}`