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PHY183-Lecture09 - R e v ie w Y e s t e r d a y 1 H o r i z...

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September 8, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Fall Semester 2006 Lecture 9 September 8, 2006 Physics for Scientists&Engineers 1 2 ! Horizontal motion: constant velocity ! Vertical motion: free fall ! Use notation convention: Review: Yesterday (1) Review: Yesterday (1) (1) x = x 0 + v x 0 t (2) v x = v x 0 2 1 0 0 2 0 0 1 0 2 2 2 0 0 (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 0 ! v x ( t = 0); v y 0 ! v y ( t = 0) September 8, 2006 Physics for Scientists&Engineers 1 3 Review: Yesterday (2) Review: Yesterday (2) ! Trajectory is a parabola in space (xy-plane) for x 0 =0 y = y 0 + v y 0 v x 0 x ! g 2 v x 0 2 x 2 y = y 0 + x tan ! 0 " g 2 v 0 2 cos 2 ! 0 x 2 or: y x 0 0 0 0 0 0 cos sin x y v v v v ! ! = = Thanks to September 8, 2006 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. v ( t ) t v x ( t ) v x 0 v y ( t ) v y 0 Slope = -g t = v y 0 / g 0 0 (1) (2 ( ) ( ) ) x x y y v t v v t v gt = = !
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September 8, 2006 Physics for Scientists&Engineers 1 5 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 September 8, 2006 Physics for Scientists&Engineers 1 6 Dependences of Velocity (1) !
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