Using dimensional analysis, how do you convert 55mi/hr to cm/sec?

Question

I don't even know where to start on this one.

Yeah, I agree that dimensional analysis isn't really needed for this, but there are worse ones I have to do. 3.68m to cm? Who can't just look at that and know the answer? Rediculous, I know, but I guess my instructer feels it's necessary to get the hang of it.

Answer 1

First, convert 55 miles to kilometers:

1 mile= 1.609 Km
55 mi = 88.495 Km

Then 1 Km = 1000 m = 100,000 cm
88.495 Km = 8,849,500 cm.

Now hr to sec:
1 hr=60 min= 3600 sec

Divide Cm /sec= 8849500/3600=2458.194

55 mi/hr = 2,458.2 cm/sec

Answer 2

Start by converting /hr to /sed

Since 1 hr = 60 min, 1 min= 60 sec,

55 mi/hr X 1 hr/60 min X 1 min/60 sec.

You now have miles/sec. Now, you need to convert miles into cm. The equalities you might use are:

1 mile = 5280 feet
1 foot = 12 inches
1 inch = 2.54 cm

You need to set up the equalities so that the unit you want to eliminate appears in the demoninator and the unit you want to retain is in the numerator. So, continuing from above,

55 mi/hr X 1 hr/60 min X 1 min/60 sec X 5280 ft/mi X 12 in/ft X 2.54 cm/in

Multiply all of those together and check that you end up with the correct units for your answer, and you're done.

Answer 3

How does this possibly require dimensional analysis? It's a simple math conversion...

55 mi/hr where 1 mile = 1.609344 kilometers
= 88.51392 km/hr
= 88,513.93 meters/hr
= 8,851,393 cm/hr
= 147523.2 cm/min
= 2458.72 cm/sec

Answer 4

55 mi = 55*5280*12*2.54 cm = 8851392 cm
1 h = 60*60 s = 3600 s
55 mi/h = 8851392/3600 cm/s = 2458.72 cm/s

1 mi =5280 ft
1 ft = 12 in
1 in = 2.54 cm
1 h = 60 min
1 min = 60 s

Answer 5

(mile)(feet/mile)(inches/ft)(cm/in)=cm
miles x 5280 x 12 x 2.54 = cm

(hour)(minutes/hr)(second/minute) = sec
hours x 60 x 60 = sec

(55 x 5280 x 12 x 2.54) / (60 x 60) = 2458.7 cm/sec
2500 cm/sec (2 significant figures)

Answer 6

Multiply: 55 mi/hr x 1hr/60min x 1min/60sec to get Y mi/sec.

Multiply: Y mi/sec x 5,280 ft/mi x 12 in/ft x 2.54 cm/in. to get Z cm/sec.

You are welcome.

Answer 7

Break it down by simple units:
55 miles/hour = ? cm/sec

mile / hour = 5280/3600 feet per mile/ seconds per hour * miles/hour = 5280/3600 feet/second

5280/3600 feet/second * 30.48 cm/foot = ((5280/3600)*30.48 cm/sec

55 (miles/hour) * 5280/3600 (feet/second) = 55 * 1.4667 (feet/second)

80.667 (feet/sec) * 30.48 (cm/foot) = 80.667 * 30.48 cm/sec

Dimensional analysis works by converting on item into an intermediate:
i.e. : miles per hour to feet per second , then feet to cm, the seconds units would remain constant, you are just changing the length units of measurement, inches to cm. 1 inch per second is the same speed as 2.54 cm per second.

1 foot = 12 inches, there are 2.54 cm in 1 inch, therefore 1 foot = 30.48 cm/foot

55 * 5280/3600( feet/second) * 30.48(cm/foot) = (55 * 5280/3600 * 30.48 )cm/second 1/30.48 (cm./foot)

? miles/hour * 5280 feet/mile * hour/3600 seconds = ? feet/second
? feet/second * 30.48 cm/foot = ? cm/second

Answer 8

That's a good question I hope you'll find reasonable answers