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2Dmotion_xy - 2D Particle Kinematics Motion in x-y...

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2D Particle Kinematics – Motion in x-y coordinates Position: Vector definition – position vector 2 2 ˆ ˆ ( ) ( ) ( ) , tan / r t x t i y t j r x y y x θ = + = + = G Velocity: average velocity 2 1 ave 2 1 r r r t t t υ Δ = = Δ G G G G , instantaneous velocity 2 2 ˆ ˆ , tan / x y x y x y dr i j dt dx dy dt dt υ υ υ y x υ υ υ υ υ α υ = = + = = = + = υ G G Acceleration: average acceleration 2 1 ave 2 1 a t t t υ υ υ Δ = = Δ G G G G , instantaneous acceleration 2 2 2 2 2 2 2 2 ˆ ˆ , tan / x y y x x y x y d d r a a i a j dt dt d d d x d y a a a a a dt dt dt dt υ υ υ β = = = + = = = = = + = G y x a a G G Projectile motion Horizontal motion – constant velocity: 0 0 0 0 0 0 cos ( cos ) x x a x x t υ υ α υ α = = = + Vertical motion – constant acceleration: 0 0 2 0 0 0 2 2 0 0 sin 1 ( sin ) 2 ( sin ) 2 ( ) y y y a g gt 0 y y t gt g y y υ υ α υ α υ υ α = − = = + = NOTE: 1. Projectile motion is determined by its initial velocity: υ 0 and α 0 .
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