8lecture2a08

8lecture2a08 - Physics 2A Lecture 8: Jan 24, 2007 Vivek...

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Physics 2A Lecture 8: Jan 24, 2007 Vivek Sharma UCSD Physics
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Relative Velocity in 1 Dimension (x) Woman walks with velocity of 1.0 m/s along train's aisle Train is moving wit h veloc What ity of 3.0 m/s is the woman' to the s veloc right ity ? According to which Observer ???
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Relative Velocity in 1 Dimension Event: Woman Two observers -cyclist (A) -on train (B) P/A P/B B/A At any instant (take a snapshot) x pos. of P rel. to frame A ; x pos. of P rel. to frame B (train) x = distance from origin of A to origin of B == B/A B/ A dx dx dx xx x & d v td t Clearly v d v t =+ = +⇒ P /A but If woma So woman's veloci n was walking in ty as seen by cyclist (A) v 1.0m opp. dir. in train v 1.0m/s 3.0m/s 2.0m /s 3.0m/s 4.0m/s /s =− + = =
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Relative Velocity in 3D A B Suppose woman walks from one side of car to another with speed of 1.0m/s . Her motion is perpendicular to direction of the aisle and the train’s motion P/A P/B B/ P/ A BB / A v r r r vv = = + + GG G G
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Relative Velocity in 3D B/A P/ P/A / B P/B B A ˆˆ v( 3 . 0 m / s ) v ( 1 vv 3 . 0 1 . 0 ) m / .0m/s) s i , j i+ j + == G G G G G 22 o B PA A / / Cyclist on ground sees woma at angle w.r.t. tr Speed of P seen by A= | v | ain's motion n moving v1 . 0 m / s : tan = 18 v (3.0m/s) (1.0m/ ) m s 3.0 /s α= α ⇒α= =+ G
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0 All projectile motion occurs in the vertical plane containing v initial vector G Projectile Motion Projectile : An object launched with some initial velocity that follows a path determined entirely by effects of gravitational acceleration g = - 9.8 m/s 2 (and air resistance) Trajectory : path of a projectile (such as from a catapult) Can decompose any projectile motion into two orthogonal and independent components - along x axis with constant velocity, a x =0 - along y axis with constant accel., a y = g Can express all relations for r, v and a in terms of components along x, y Projectile motion is superposition of these seperate and indep axi ende s nt motio s.
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This note was uploaded on 05/08/2008 for the course PHYS 2A taught by Professor Hicks during the Winter '07 term at UCSD.

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8lecture2a08 - Physics 2A Lecture 8: Jan 24, 2007 Vivek...

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