ProblemSet1 - Problem Set 1 Physics 1116 : Due Friday,...

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Problem Set 1 Physics 1116 : Due Friday, 09/03/2010 Please write the names of any classmates with whom you discussed the homework problems at the top of your problem set Problems are on BOTH sides of the page 1. Given two vectors, ~ A = 6 ˆ i +3 ˆ j - 9 ˆ k and ~ B = 9 ˆ i - 8 ˆ j +2 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. A particle moves along the curve y = A sin( Cx ) (where C has the value of 1 radian / meter). Its x position in meters as a function of time is x ( t ) = Bt 2 , where B has the units of meters / sec 2 . (a) Express the vector position as a function of time in the form
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ProblemSet1 - Problem Set 1 Physics 1116 : Due Friday,...

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