An Introduction To Mechanics

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Problem Set 1 Physics 116 : Due Friday, 02/01/2008 1. Given two vectors, ~ A = 7 ˆ i + 9 ˆ j - 4 ˆ k and ~ B = 4 ˆ i - 3 ˆ j + 12 ˆ k , find the following quantities : (a) ~ A + ~ B (b) ~ A - ~ B (c) ~ A × ~ B (d) ~ A · ~ B (e) The angle, θ , 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) d dt ( c ~ A ) = dc dt ~ A + c d ~ A dt (b) d dt ( ~ A · ~ B ) = d ~ A dt · ~ B + ~ A · d ~ B dt (c) d dt ( ~ A × ~ B ) = d ~ A dt × ~ B + ~ A × d ~ B dt 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 measur- ing 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
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