Question

Can somebody help me understand how to find the answer to this dimensional analysis question?? The screenshot is in the replies.

Answer 1

@Vuriffy

Answer 2

okay what do you need help with exactly

Answer 3

Suppose there are \(x\text{ unit}_1\) for every \(y\text{ unit}_2\). Then to convert \(z\) of one unit to the other, say from \(\text{unit}_1\) to \(\text{unit}_2\), the conversion factor would be \(\dfrac{y\text{ unit}_2}{x\text{ unit}_1}\):
\[(z\cancel{\text{ unit}_1})\times\frac{y\text{ unit}_2}{x\cancel{\text{ unit}_1}}=\frac{zy}{x}\text{ unit}_2\]We don't know what you're trying to convert, so I'll just give a quick example. Say you're asked to convert \(12\text{ mph}\) to \(\text{km/h}\). Then the conversion can be carried out by computing
\[\frac{12\cancel{\text{ miles}}}{1\text{ hour}}\times\frac{y\text{ km}}{x\cancel{\text{ miles}}}=12\frac{y}{x}\text{ km/h}\]You're told that the conversion factor from miles to kilometers is \(1.6093\), so
\[12\text{ mph}=12\times1.6093\text{ km/h}\approx 19.3\text{ km/h}\]