Question

Convert 75mph to km/s. According to the text, the answer is 0.034 km/s (or 3.4x10^-2 km/s). I have no idea how you arrive at the answer. I know you have to keep canceling out the units until you've reached the desired one, but I can't figure out how.

1. 75 mi/hr
2. Convert miles to feet and cancel out miles >> 75 mi/hr x 5280 ft/mi
But where did the 5280 come from?

Answer 1

mph is short for miles per hour, or , written as a fraction
\[ \frac{miles}{hour} \]
you want km/sec
tackle the top and bottom separately
first the top: miles
you want km
the trick is to think like in algebra (if you know how)
\[ miles \cdot \frac{km}{miles} \]
and like in algebra, the miles can be cancelled
\[\cancel{ miles} \cdot \frac{km}{\cancel{ miles}} =km\]

that means we need a fraction that tells us the number of km in a mile
we look that up (or remember it)
\[ \frac{1.609344 \ km}{1 \ mile} \]
use that fraction to convert your miles:
\[ 75 \ miles \cdot \frac{1.609344 \ km}{1 \ mile} \]
can you find how many km that is ?

Answer 2

once you can do this, we can do the same thing using feet. same idea, but more steps