I just do not understand dimensional analysis. Can anybody explain this question:

32 cm = ?m
---- ----
s min

Although your dimension labels to not seem to be lined up correctly, it looks like you are being asked to convert 32 cm/s to ? meters/minute. You can do that by multiplying 32 cm/s by (1 m/100 cm)* (60 s/min), as follows:
32 cm/s x (1 m/100 cm) x (60 s/min)
= 19.2 m/min
Dimensions that appear in both numerators and denominators cancel out. Note that the numerator and denominator of the conversion factors correspond to the same actual amount of the physical quantity (i.e, 60 s = 1 minute of time)

Thank you drwls.
That helps so much!

You're welcome! I'm glad I could help you understand dimensional analysis. It's a useful method for converting between different units and keeping track of the dimensions of quantities.

In this specific example, you were given a measurement of 32 cm/s and were asked to convert it to meters per minute. To do this, you can use conversion factors to cancel out the unwanted units and replace them with the desired units.

First, let's examine the given units: cm/s. To convert cm to meters, we can use the conversion factor 1 m/100 cm. This means that there are 1 meter in every 100 centimeters. By multiplying our original measurement by this conversion factor, the cm unit will cancel out and we'll have the measurement in meters:

32 cm/s * (1 m/100 cm) = 0.32 m/s

Now, to convert seconds to minutes, we can use the conversion factor 1 min/60 s. This means that there are 1 minute in every 60 seconds. By multiplying our previous result by this conversion factor, the s unit will cancel out and we'll have the measurement in meters per minute:

0.32 m/s * (1 min/60 s) = 0.32 m/s * (1 min/60 s) = 19.2 m/min

So, 32 cm/s is equivalent to 19.2 m/min. Remember, when using dimensional analysis, it's important to keep track of the units and ensure they cancel out appropriately.

I hope this explanation further clarifies how to approach dimensional analysis. If you have any more questions, feel free to ask!