Simple Nature - Light and Matter

⊲ First we convert the equation into a proportionality by throwingout k, which is the same for both vehicles:C ∝ w 4Next we convert this proportionality to a statement about ratios:( )C 41 w1= ≈ 29, 000C 2 w 2Since the gas taxes paid by the trucker are nowhere near 29,000times more than those I pay to drive my Fit the same distance, thefederal government is effectively awarding a massive subsidy to thetrucking company. Plus my Fit is cuter.Examples with solutions — p. 51, #32; p. 51, #33; p. 52, #38;p. 49, #17Problems you can check at lightandmatter.com/area1checker.html — p. 52, #37; p. 52, #39; p. 121, #24; p. 122, #27; p. 119,#9; p. 288, #33. Vector additionsubsection 3.4.3, p. 199Example: The ∆r vector from San Diego to Los Angeles hasmagnitude 190 km and direction 129 ◦ counterclockwise from east.The one from LA to Las Vegas is 370 km at 38 ◦ counterclockwisefrom east. Find the distance and direction from San Diego to LasVegas.⊲ Graphical addition is discussed on p. 199. Here we concentrate onanalytic addition, which involves adding the x components to findthe total x component, and similarly for y. The trig needed in orderto find the components of the second leg (LA to Vegas) is laid outin figure l on p. 197 and explained in detail in example 60 on p. 197:∆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 toavoid accumulating too much rounding error.) Once we understandthe trig for one example, we don’t need to reinvent the wheel everytime. The pattern is completely universal, provided that we firstmake sure to get the angle expressed according to the usual trigconvention, counterclockwise from the x axis. Applying the patternto the first leg, we have:∆x 1 = (190 km) cos 129 ◦ = −120 km∆y 1 = (190 km) sin 129 ◦ = 148 kmFor 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 .906 Chapter 13 Quantum Physics