An Introduction To Mechanics

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Unformatted text preview: Problem Set 1 Physics 116 : Due Friday, 02/01/2008 ^ ^ 1. Given two vectors, A = 7^ + 9^ - 4k and B = 4^ - 3^ + 12k, find the following i j i j quantities : (a) A + B (b) A - B (c) A B (d) A B (e) The angle, , between A and B (f) A unit vector, c, which is normal to the plane in which both A and B lie 2. Prove the three identities : (a) (b) (c) d (cA) dt d (A dt d (A dt = dc A dt A + c ddt B) = dA dt B+A dB dt dB dt B) = dA dt B+A 3. K&K, Problem 1.10 4. The Global Positioning System (GPS) works by using an array of orbiting satellites at precisely known locations which send out synchronized timing pulses. From measuring the time it takes for a signal to travel from a satellite to your unit, and doing this for various satellites, your position can then be precisely triangulated. Let's assume that you are in Collegetown {Latitude = 42.48 , Longitude = 76.47 }, and your unit locks onto 4 satellites which have latitude and longitude of : Sata = {30 ,80 }, Satb = {60 ,50 }, Satc = {20 ,60 }, and Satd = {50 ,90 }. What is the delay that your GPS unit measures for each satellite's signal? For this problem, assume that the earth is a perfect sphere of radius 6360 km, and that the satellites are all exactly 20,000 km above the surface of the planet. The signals are radio waves transmitted at the speed of light (3 108 m/s), which is very fast, so ignore the motion of the earth or satellites. 5. K&K, Problem 1.13 6. K&K, Problem 1.16 7. K&K, Problem 1.19 8. K&K, Problem 1.21 1 ...
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