.First we convert the equation into a proportionality by throwing
outk, which is the same for both vehicles:
C∝w^4
Next we convert this proportionality to a statement about ratios:
C 1
C 2=
(
w 1
w 2) 4
≈29, 000
Since the gas taxes paid by the trucker are nowhere near 29,000
times more than those I pay to drive my Fit the same distance, the
federal government is effectively awarding a massive subsidy to the
trucking company. Plus my Fit is cuter.
Examples with solutions — p. 51, #32; p. 51, #33; p. 52, #38;
p. 49, #17
Problems you can check atlightandmatter.com/area1checker.
html— p. 52, #37; p. 52, #39; p. 123, #24; p. 124, #27; p. 121,
#9; p. 294, #3- Vector addition
subsection 3.4.3, p. 203
Example: The ∆rvector from San Diego to Los Angeles has
magnitude 190 km and direction 129◦counterclockwise from east.
The one from LA to Las Vegas is 370 km at 38◦counterclockwise
from east. Find the distance and direction from San Diego to Las
Vegas.
.Graphical addition is discussed on p. 203. Here we concentrate on
analytic addition, which involves adding thexcomponents to find
the totalxcomponent, and similarly fory. The trig needed in order
to find the components of the second leg (LA to Vegas) is laid out
in figure l on p. 201 and explained in detail in example 60 on p. 201:
∆x 2 = (370 km) cos 38◦= 292 km
∆y 2 = (370 km) sin 38◦= 228 km
(Since these are intermediate results, we keep an extra sig fig to
avoid accumulating too much rounding error.) Once we understand
the trig for one example, we don’t need to reinvent the wheel every
time. The pattern is completely universal, provided that we first
make sure to get the angle expressed according to the usual trig
convention, counterclockwise from thexaxis. Applying the pattern
to the first leg, we have:
∆x 1 = (190 km) cos 129◦=−120 km
∆y 1 = (190 km) sin 129◦= 148 km
For the vector directly from San Diego to Las Vegas, we have
∆x= ∆x 1 + ∆x 2 = 172 km
∆y= ∆y 1 + ∆y 2 = 376 km.
1016 Chapter 14 Additional Topics in Quantum Physics