GGRA30H3 Study Guide - Geocoding, Stochastic Process, Census Tract

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28 Apr 2012

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Geocoding: more accurate than using tiger to approx- imate addresses. No geocoding is pos- sible if address not listed, post office box, or incomplete, or wrong county assigned. Parel : a plot of land, usually a division of a larger are. A semi-log model of blood lead level (lead exposure) for proper- ties with screened children. The regression model: with the relationship between some outcome and one factor. Suppose, for example, we want to know something about how education level affects income, Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in a geographic space. Classic spatial autocorrelation statistics include moran"s and geary"s and getis"g. Classic spatial autocorrelation statistics compare the spatial weights to the covariance relationship at pairs of locations. Partitioning ofgeographic title (1) coverage and no over lap essellation is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps.

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Learning Goal: To understand length contraction and timedilation.

An inertial frame of reference is one in which Newton's laws hold.Any frame of reference that moves at a constant speed relative toan inertial frame of reference is also an inertial frame. Theproper length l_0 of an object is defined to be the length of theobject as measured in the object's rest frame. If the length of theobject is measured in any other inertial frame, moving with speed urelative to the object's rest frame (in a direction parallel tol_0), the resulting length l is given by the length contractionequation

l = l_0\sqrt{1-\frac{u^2}{c^2}} ,

where c is the speed of light. Similarly, if two events occur atthe same spatial point in a particular reference frame, and anobserver at rest in this frame measures the time interval betweenthese two events, the time interval so measured is defined to bethe proper time Delta t_0. When the time interval is measured inany other inertial frame, again moving with speed u relative to thefirst frame, the resulting time interval Delta t is given by thetime dilation equation

\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{u^2}{c^2}}} .

a. Suppose that you measure the length of a spaceship, at restrelative to you, to be 400 \rm m. How long will you measure it tobe if it flies past you at a speed of u = 0.75c?
Express the length l in meters to three significant figures.

b. The spaceship from Part A has a large clock attached to itsside. This clock ran at the same rate as your watch when you werein the same reference frame. How much time Delta t will pass onyour watch as 80 \rm s passes on the clock attached to theship?
Express your answer in seconds to three significant figures.

c. Two spaceships, named A and B, are flying toward each other withrelative speed 0.800c. If the captain of ship A fires a missile,counts 10.0 \rm s on his watch, and then fires a second missile,how much time Delta t will the captain of ship B measure to havepassed between the firing of the two missiles?
Express your answer in seconds to three significant figures.

d. The captain of ship B knows that ship A uses 2-m-long missiles.She measures the length of the first missile, once it has finishedaccelerating, and finds it to be only 0.872 \rm m long. What is thespeed u of the missile, relative to ship B?
Express your answer in meters per second to three significantfigures. Use c = 3 \times 10^8 \; \rm m/s.

Please answer fully... thank you

(There is a arrow symbol over the r in this problem denotingthat it is a vector) Suppose there is a charge distribution p(r,t),which has spherical symmetry at anytime.In other words, p(r,t) onlydepends on the magnitude or r and t, but not on the angle of r. Thevelocity distribution of charges is spherically symmetrical, i.ev(r,t) is along the radial direction and only depends on theabsolute value of r and t.

1) By using symmetry analysis, determine the distribution of B(r)(Both B and r have arrow symbols above them denoting they arevectors) Hint: you also need to know the fact that no magneticmonopoles exist.

2) What's the displacement current distributionJd=(1/(4p))(dE/(dt)) (Note that there is an arrow above J and E inthe previous equation noting that these are vectors and d is asubscript) Whats the relationship between Jd (the j has an arrowover it indicating it is a vector and d is a subscript) and theactual current density J (with an arrow over it indicating it is avector J)? Explain why your result in part 1) is correct eventthough it looks counter intuitive.

GGRA30H3 Study Guide - Geocoding, Stochastic Process, Census Tract

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