Question

Which of the following would be a correct use of dimensional analysis to convert 45 mph to feet per sec? a.
`(45 \: miles)/(hour) * (1mile)/(5280ft) * (1hour)/(60min) * (1min)/(60sec)`b.
`(45miles)/(hour) * (5280ft)/(1mile) * (1hour)/(60min) * (1min)/(60sec)`c.
`(45miles)/(1hour) * (1ft)/(5280miles) * (1hour)/(60min) * (1min)/(60sec)`

Answer 1

We have the following conversion regarding that:

1 mile = 5280.02 feet

1 hour = 3600 sec

Then, to convert 45 mph to feet per sec, we have:

`45(m)/(h)\cdot5280.02(f)/(m)\cdot(1h)/(3600s)\Rightarrow(45\cdot5280.02)/(3600)ft/\sec`

The units m/m = 1, h/h =1, and then the units remaining were feet / sec.

Then, we have:

`(45\cdot5280.02)/(3600)=66.00025ft/\sec`

Then, the two conversions are:

• 45 m/h * 5280.0 feet/mile, and

,

• 1 h/ 3600sec = (1 hour/60min) * (1 min/60sec).