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lecture06 - Phy 2053 Chapter 3 Vectors and Motion in 2-D...

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1 Phy 2053 Announcements Phy 2053 Chapter 3 Vectors, and Motion in 2-D Thursday, Sept. 10, 2008—Gary Ihas What to do? Zero v at the Top Δ x 2 v v 2 0 2 a + = v = 0 Throw ball up -initial velocity non-zero and positive Instantaneous velocity = 0 at maximum height =0 Δ x x Can be given v 0 and ask for OR vice versa Vectors let us keep track of our way in any number of dimensions by carrying all the numbers-components-we need in one symbol square6 Here is a vector that shows us going at an angle Θ with the x axis square6 It is useful to use rectangular components to manipulate vectors square6 These are the projections of the vector along the x- and y-axes A x and A y A x and A y are scalars Vector Components square6 The x-component of a vector is the projection along the x-axis cos A A θ = x x θ = uur ur cos A A x square4 The y-component of a vector is the projection along the y-axis sin y A A θ = y θ = uur ur sin A A y These equations are valid only if θ is measured with respect to the x-axis x y = + r r r A A A Then, Graphically Adding Vectors square6 When you add vectors, just put the tail of one on the head on the next… square6 The resultant is drawn from the origin of the first vector to the end of the last vectorVectors obey the commutative law of addition The order in which the vectors are added doesn’t affect the result Note that vectors are unchanged by being moved
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