Question

a runner ran 100 meters in 10.49 seconds. using dimensional analysis and using 3.28 feet per meter and 5,280 feet per mile, how fast did they do this in miles per hour? Thanks

Answer 1

hello

to solve this, we need to simply convert meters and seconds unit to miles and hour

1 mile = 1609.34meter

x mile = 100 m

cross multiply both sides

`\begin{gathered} 1609.34* x=1*100 \\ 1609.34x=100 \\ \text{divide both sides by the coefficient of x} \\ (1609.34x)/(1609.34)=(100)/(1609.34) \\ x=0.062 \end{gathered}`

now we can say the runner ran 0.062 miles in 10.49sec

we can proceed to convert the seconds unit to hour

60 seconds = 1 min

60 minutes = 1 hour

1 hour = 60 x 60 seconds

1 hour = 3600s

0.062miles in 10.49 sec

x miles in 3600s

`\begin{gathered} 0.062=10.49 \\ x=3600 \\ \text{cross multiply both sides} \\ 10.49* x=3600*0.062 \\ 10.49x=223.2 \\ \text{divide both sides by the coefficient of x} \\ (10.49x)/(10.49)=(223.2)/(10.49) \\ x=21.277\approx21.28 \end{gathered}`

at this pace, the runner ran 21.28 miles per hour