Posted by Brandon on Thursday, February 19, 2009 at 8:20pm.
Here is the way to do these. Do them by dimensional analysis and be sure the units you don't want cancel and the unit(s) you want to keep don't cancel.
For km/hr we want three conversions; one for km to m and the other for hr to min and a third one for min to seconds.
What are the conversions?
1 km = 1000 m
60 min = 1 hour
60 sec = 1 minute.
Now the factors can be set up either of two ways.
1 km = 1000 m can be set up to be
(1 km/1000 m) OR (1000 m/1 km).
Likewise the others can be set up one of two ways.
(60 min/1 hr) or (1 hr/60 min) and
(60 sec/1 min) or (1 min/60 sec).
In the conversion, you want to cancel the units you have and keep the units which the problem asks for. Always start with the number given.
95.4 km/hr x factor x factor x factor.
Let's just worry about the first factor.
95.4 km/hr x (now how do we know how to use the factor? remember we want km to cancel and we want the answer to be in m). So,
95.4 km/hr x (1000 m/km)...
Note that km is in the numerator AND it is in the denominator; therefore, the km cancels and we have in its place m. So the first factor has converted from km/hr to m/hr. What would happen if we turned the factor over and used 1 km/1000 m)? Let's try it.
95.4 km/hr x (1 km/1000 m) = and you notice km are the numerator of BOTH terms and nothing cancels. If nothing cancels we know we should have done it the other way.
Now the second and third terms.
95.4 km/hr x (1000 m/km) x (1 hr/60 min) x (1 min/60 sec) = ??
Let's see how the factors work.
km in the numerator cancels with km in the denominator of the first factor (giving us m/hr). The second factor has hr in the numerator and that cancels with hr in the denominator of the original number. Now we have converted from km/hr to m/hr to m/min. The third factor has min in the numerator and that cancels with min in the second factor. Now we have conerted from km/hr to m/min to m/sec. And m/sec is what we want. All the units cancel EXCEPT what we wanted; i.e., m/sec. I get 26.5 m/sec. I hope this helps. It takes a little practice but the method is fool proof.