Use dimensional analysis to convert 92 feet per minute to meters per second.

Step-by-step solution

1. 1

   List the two conversion factors needed. The quantity has a length unit on top and a time unit underneath, so both must be replaced:

   $1\ \text{ft}=0.3048\ \text{m}\qquad\text{(exact by definition)},\qquad 1\ \text{min}=60\ \text{s}.$

2. 2

   Write each factor as a fraction equal to $1$, oriented so the unwanted unit cancels. Feet must cancel from the numerator, and minutes must cancel from the denominator:

   $92\ \frac{\cancel{\text{ft}}}{\cancel{\text{min}}}\times\frac{0.3048\ \text{m}}{1\ \cancel{\text{ft}}}\times\frac{1\ \cancel{\text{min}}}{60\ \text{s}}.$

   Choosing the orientation by cancellation, rather than by guessing whether to multiply or divide, is the whole point of dimensional analysis.

3. 3

   Multiply the numerators.

   $92\times 0.3048=28.0416\ \text{m per minute}.$

   This intermediate value is a legitimate answer in m/min and worth keeping as a checkpoint.

4. 4

   Divide by the 60 seconds in a minute.

   $\frac{28.0416}{60}=0.46736\ \frac{\text{m}}{\text{s}}.$

5. 5

   Sanity-check the magnitude. A metre is about $3.28$ ft, so $92$ ft/min is roughly $28$ m/min, and dividing by $60$ should land just under half a metre per second — which it does. Reversing the calculation, $0.46736\times 60/0.3048=92.000$ ft/min exactly.