Products of rations to convert meters per second to miles per hour

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In summary: The m's cancel, leaving only mi/h, as desired.In summary, the correct product of ratios for converting m/s to mi/h is [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h].
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new^2^physics
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Homework Statement



Which of the following products of ratios gives the conversion factors to convert meters per second (m/s) to miles per hour (mi/hr)

Homework Equations



a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]

The Attempt at a Solution



I will try to solve all these EXCLUDING THE NUMBERS, so I can focus on units and how they cancel each other out.

a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
= in/mi x cm/in = cm/mi x cm/in = cm2/ mi.in... WRONG
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
= in/mi x in/cm = in2/mi.cm = WRONG
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
= in/mi x cm/in = cm/mi x cm/m = cm2/ mi.m - WRONG
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x cm/m = mi/m x s/h... hmmm WRONG??
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x m/cm = mi.m/cm2 WRONG

Basically I am beyond confused and would deeply appreciate any direction or help

THANK YOU!
 
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  • #2
new^2^physics said:

Homework Statement



Which of the following products of ratios gives the conversion factors to convert meters per second (m/s) to miles per hour (mi/hr)

Homework Equations



a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]

The Attempt at a Solution



I will try to solve all these EXCLUDING THE NUMBERS, so I can focus on units and how they cancel each other out.

a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
= in/mi x cm/in = cm/mi x cm/in = cm2/ mi.in... WRONG
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
= in/mi x in/cm = in2/mi.cm = WRONG
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
= in/mi x cm/in = cm/mi x cm/m = cm2/ mi.m - WRONG
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x cm/m = mi/m x s/h... hmmm WRONG??
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x m/cm = mi.m/cm2 WRONG

Basically I am beyond confused and would deeply appreciate any direction or help

THANK YOU!

d is correct. I couldn't quite follow your work, but you reduced it properly to mi/m x s/h. You then only needed to multiply by m/s to get mi/h.
 

Related to Products of rations to convert meters per second to miles per hour

1. How do you convert meters per second to miles per hour?

To convert meters per second to miles per hour, you can use the formula: miles per hour = meters per second * 2.237. This formula is derived from the fact that 1 meter per second is equivalent to 2.237 miles per hour.

2. What is the conversion factor from meters per second to miles per hour?

The conversion factor from meters per second to miles per hour is 2.237. This means that to convert from meters per second to miles per hour, you need to multiply the value in meters per second by 2.237.

3. Can you provide an example of converting meters per second to miles per hour?

For example, if you have a speed of 10 meters per second, the conversion to miles per hour would be: 10 meters per second * 2.237 = 22.37 miles per hour. So, 10 meters per second is equivalent to 22.37 miles per hour.

4. Is there a simpler way to convert meters per second to miles per hour?

Yes, there is a simpler way to convert meters per second to miles per hour. You can use an online conversion tool or a calculator to directly convert the values without having to use the formula. You can also refer to conversion charts for quick conversions.

5. Are there any common mistakes to avoid when converting meters per second to miles per hour?

One common mistake to avoid is using the wrong conversion factor. Make sure to use the correct conversion factor of 2.237 when converting from meters per second to miles per hour. Another mistake is forgetting to include the proper units in the final answer. Always make sure to include the units of measurement in the converted value.

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