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# W3.1 - Physics for Scientists&Engineers 1 1 Physics for...

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Unformatted text preview: January 18, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2008 Lecture 9 January 18, 2008 Physics for Scientists&Engineers 1 2 Horizontal motion: constant velocity Vertical motion: free fall Use notation convention: Review: Previous Lecture (1) Review: Previous Lecture (1) (1) x = x + v x t (2) v x = v x 2 1 2 1 2 2 2 (3) (4) ( ) (5) (6) (7) 2 ( ) y y y y y y y y y y y v t gt v v gt y y v t v v v v v g y y = + ! = ! = + = + = ! ! v x ! v x ( t = 0); v y ! v y ( t = 0) January 18, 2008 Physics for Scientists&Engineers 1 3 Review: Previous Lecture (2) Review: Previous Lecture (2) Trajectory is a parabola in xy-plane (here special case of x = 0 ) y = y + v y v x x ! g 2 v x 2 x 2 y = y + x tan ! " g 2 v 2 cos 2 ! x 2 or: y x cos sin x y v v v v ! ! = = Since January 18, 2008 Physics for Scientists&Engineers 1 4 v(t) v(t) Look at x- and y-components separately Horizontal component of the velocity stays constant in time -> horizontal line Vertical component falls in time, with slope -g Note: if vertical velocity starts positive, it will reach a point at which it is 0 (which is also the highest point in the trajectory!) v ( t ) t v x ( t ) v x v y ( t ) v y S l o p e =- g t = v y / g (1) (2 ( ) ( ) ) x x y y v t v v t v gt = = ! January 18, 2008 Physics for Scientists&Engineers 1 5 v(t) and Trajectory v(t) and Trajectory Superimpose snapshots of velocity vectors on trajectory at different times • Green arrows : horizontal v-component • Red arrows : vertical v-component • Blue arrows : velocity vector Important: velocity vector forms tangent at every point of trajectory Note: at apex of trajectory, v y changes sign January 18, 2008 Physics for Scientists&Engineers 1 6 In-Class Exercise 1 In-Class Exercise 1 In-class exercise: At the top of the trajectory of any projectile,...
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W3.1 - Physics for Scientists&Engineers 1 1 Physics for...

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