05 - 2D particle kinematics - Motion in x-y coordinates

# 05 - 2D particle kinematics - Motion in x-y coordinates -...

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2D Particle Kinematics – Motion in x-y coordinates Position: Vector definition – position vector 22 ˆˆ () () , tan / rt xti yt j r x y y x θ =+ = + = G Velocity: average velocity 21 ave rr r ttt υ Δ == Δ G G G G , instantaneous velocity , / xy x yx y dr ij dt dx dy dt dt υυ y x α ==+ ⇒= = = + = G G Acceleration: average acceleration ave a tt t Δ Δ G G G G , instantaneous acceleration 2 2 / y x x y dd r aa i a j dt dt d d dx dy a a a dt dt dt dt β ⇒= = = = = + = G y x a a G G Projectile motion Horizontal motion – constant velocity: 00 0 0 cos (c o s) x x a x xt υυ α = = Vertical motion – constant acceleration: 2 0 sin 1 (s i n ) 2 i n ) 2 ( ) y y y ag gt 0 y yt g t g yy υα υυα =− NOTE: 1. Projectile motion is determined by its initial velocity: υ 0 and α 0 . 2. The initial angle α 0 is positive/negative if the projectile is launched above/below the horizontal.
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## This note was uploaded on 10/17/2009 for the course PHYS 2305 taught by Professor Tschang during the Spring '08 term at Virginia Tech.

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05 - 2D particle kinematics - Motion in x-y coordinates -...

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